/*******************************************************************************
*                                                                              *
* Author    :  Angus Johnson                                                   *
* Version   :  6.4.2                                                           *
* Date      :  27 February 2017                                                *
* Website   :  http://www.angusj.com                                           *
* Copyright :  Angus Johnson 2010-2017                                         *
*                                                                              *
* License:                                                                     *
* Use, modification & distribution is subject to Boost Software License Ver 1. *
* http://www.boost.org/LICENSE_1_0.txt                                         *
*                                                                              *
* Attributions:                                                                *
* The code in this library is an extension of Bala Vatti's clipping algorithm: *
* "A generic solution to polygon clipping"                                     *
* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *
* http://portal.acm.org/citation.cfm?id=129906                                 *
*                                                                              *
* Computer graphics and geometric modeling: implementation and algorithms      *
* By Max K. Agoston                                                            *
* Springer; 1 edition (January 4, 2005)                                        *
* http://books.google.com/books?q=vatti+clipping+agoston                       *
*                                                                              *
* See also:                                                                    *
* "Polygon Offsetting by Computing Winding Numbers"                            *
* Paper no. DETC2005-85513 pp. 565-575                                         *
* ASME 2005 International Design Engineering Technical Conferences             *
* and Computers and Information in Engineering Conference (IDETC/CIE2005)      *
* September 24-28, 2005 , Long Beach, California, USA                          *
* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *
*                                                                              *
*******************************************************************************/

/*******************************************************************************
*                                                                              *
* This is a translation of the Delphi Clipper library and the naming style     *
* used has retained a Delphi flavour.                                          *
*                                                                              *
*******************************************************************************/

#include "clipper.hpp"
#include <cmath>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstring>
#include <cstdlib>
#include <ostream>
#include <functional>

namespace ClipperLib
{

  static double const pi = 3.141592653589793238;
  static double const two_pi = pi * 2;
  static double const def_arc_tolerance = 0.25;

  enum Direction
  {
    dRightToLeft, dLeftToRight
  };

  static int const Unassigned = -1;  //edge not currently 'owning' a solution
  static int const Skip = -2;        //edge that would otherwise close a path

#define HORIZONTAL (-1.0E+40)
#define TOLERANCE (1.0e-20)
#define NEAR_ZERO(val) (((val) > -TOLERANCE) && ((val) < TOLERANCE))

  struct TEdge
  {
    IntPoint Bot;
    IntPoint Curr; //current (updated for every new scanbeam)
    IntPoint Top;
    double Dx;
    PolyType PolyTyp;
    EdgeSide Side; //side only refers to current side of solution poly
    int WindDelta; //1 or -1 depending on winding direction
    int WindCnt;
    int WindCnt2; //winding count of the opposite polytype
    int OutIdx;
    TEdge *Next;
    TEdge *Prev;
    TEdge *NextInLML;
    TEdge *NextInAEL;
    TEdge *PrevInAEL;
    TEdge *NextInSEL;
    TEdge *PrevInSEL;
  };

  struct IntersectNode
  {
    TEdge *Edge1;
    TEdge *Edge2;
    IntPoint Pt;
  };

  struct LocalMinimum
  {
    cInt Y;
    TEdge *LeftBound;
    TEdge *RightBound;
  };

  struct OutPt;

//OutRec: contains a path in the clipping solution. Edges in the AEL will
//carry a pointer to an OutRec when they are part of the clipping solution.
  struct OutRec
  {
    int Idx;
    bool IsHole;
    bool IsOpen;
    OutRec *FirstLeft;  //see comments in clipper.pas
    PolyNode *PolyNd;
    OutPt *Pts;
    OutPt *BottomPt;
  };

  struct OutPt
  {
    int Idx;
    IntPoint Pt;
    OutPt *Next;
    OutPt *Prev;
  };

  struct Join
  {
    OutPt *OutPt1;
    OutPt *OutPt2;
    IntPoint OffPt;
  };

  struct LocMinSorter
  {
    inline bool operator()(const LocalMinimum &locMin1, const LocalMinimum &locMin2)
    {
      return locMin2.Y < locMin1.Y;
    }
  };

//------------------------------------------------------------------------------
//------------------------------------------------------------------------------

  inline cInt Round(double val)
  {
    if ((val < 0))
      return static_cast<cInt>(val - 0.5);
    else
      return static_cast<cInt>(val + 0.5);
  }
//------------------------------------------------------------------------------

  inline cInt Abs(cInt val)
  {
    return val < 0 ? -val : val;
  }

//------------------------------------------------------------------------------
// PolyTree methods ...
//------------------------------------------------------------------------------

  void PolyTree::Clear()
  {
    for (PolyNodes::size_type i = 0; i < AllNodes.size(); ++i)
      delete AllNodes[i];
    AllNodes.resize(0);
    Childs.resize(0);
  }
//------------------------------------------------------------------------------

  PolyNode *PolyTree::GetFirst() const
  {
    if (!Childs.empty())
      return Childs[0];
    else
      return 0;
  }
//------------------------------------------------------------------------------

  int PolyTree::Total() const
  {
    int result = (int) AllNodes.size();
    //with negative offsets, ignore the hidden outer polygon ...
    if (result > 0 && Childs[0] != AllNodes[0])
      result--;
    return result;
  }

//------------------------------------------------------------------------------
// PolyNode methods ...
//------------------------------------------------------------------------------

  PolyNode::PolyNode() : Parent(0), Index(0), m_IsOpen(false)
  {
  }
//------------------------------------------------------------------------------

  int PolyNode::ChildCount() const
  {
    return (int) Childs.size();
  }
//------------------------------------------------------------------------------

  void PolyNode::AddChild(PolyNode &child)
  {
    unsigned cnt = (unsigned) Childs.size();
    Childs.push_back(&child);
    child.Parent = this;
    child.Index = cnt;
  }
//------------------------------------------------------------------------------

  PolyNode *PolyNode::GetNext() const
  {
    if (!Childs.empty())
      return Childs[0];
    else
      return GetNextSiblingUp();
  }
//------------------------------------------------------------------------------

  PolyNode *PolyNode::GetNextSiblingUp() const
  {
    if (!Parent) //protects against PolyTree.GetNextSiblingUp()
      return 0;
    else if (Index == Parent->Childs.size() - 1)
      return Parent->GetNextSiblingUp();
    else
      return Parent->Childs[Index + 1];
  }
//------------------------------------------------------------------------------

  bool PolyNode::IsHole() const
  {
    bool result = true;
    PolyNode *node = Parent;
    while (node)
    {
      result = !result;
      node = node->Parent;
    }
    return result;
  }
//------------------------------------------------------------------------------

  bool PolyNode::IsOpen() const
  {
    return m_IsOpen;
  }
//------------------------------------------------------------------------------

#ifndef use_int32

//------------------------------------------------------------------------------
// Int128 class (enables safe math on signed 64bit integers)
// eg Int128 val1((long64)9223372036854775807); //ie 2^63 -1
//    Int128 val2((long64)9223372036854775807);
//    Int128 val3 = val1 * val2;
//    val3.AsString => "85070591730234615847396907784232501249" (8.5e+37)
//------------------------------------------------------------------------------

  class Int128
  {
  public:
    ulong64 lo;
    long64 hi;

    Int128(long64 _lo = 0)
    {
      lo = (ulong64) _lo;
      if (_lo < 0)
        hi = -1;
      else
        hi = 0;
    }


    Int128(const Int128 &val) : lo(val.lo), hi(val.hi)
    {
    }

    Int128(const long64 &_hi, const ulong64 &_lo) : lo(_lo), hi(_hi)
    {
    }

    Int128 &operator=(const long64 &val)
    {
      lo = (ulong64) val;
      if (val < 0)
        hi = -1;
      else
        hi = 0;
      return *this;
    }

    bool operator==(const Int128 &val) const
    {
      return (hi == val.hi && lo == val.lo);
    }

    bool operator!=(const Int128 &val) const
    {
      return !(*this == val);
    }

    bool operator>(const Int128 &val) const
    {
      if (hi != val.hi)
        return hi > val.hi;
      else
        return lo > val.lo;
    }

    bool operator<(const Int128 &val) const
    {
      if (hi != val.hi)
        return hi < val.hi;
      else
        return lo < val.lo;
    }

    bool operator>=(const Int128 &val) const
    {
      return !(*this < val);
    }

    bool operator<=(const Int128 &val) const
    {
      return !(*this > val);
    }

    Int128 &operator+=(const Int128 &rhs)
    {
      hi += rhs.hi;
      lo += rhs.lo;
      if (lo < rhs.lo)
        hi++;
      return *this;
    }

    Int128 operator+(const Int128 &rhs) const
    {
      Int128 result(*this);
      result += rhs;
      return result;
    }

    Int128 &operator-=(const Int128 &rhs)
    {
      *this += -rhs;
      return *this;
    }

    Int128 operator-(const Int128 &rhs) const
    {
      Int128 result(*this);
      result -= rhs;
      return result;
    }

    Int128 operator-() const //unary negation
    {
      if (lo == 0)
        return Int128(-hi, 0);
      else
        return Int128(~hi, ~lo + 1);
    }

    operator double() const
    {
      const double shift64 = 18446744073709551616.0; //2^64
      if (hi < 0)
      {
        if (lo == 0)
          return (double) hi * shift64;
        else
          return -(double) (~lo + ~hi * shift64);
      } else
        return (double) (lo + hi * shift64);
    }

  };
//------------------------------------------------------------------------------

  Int128 Int128Mul(long64 lhs, long64 rhs)
  {
    bool negate = (lhs < 0) != (rhs < 0);

    if (lhs < 0)
      lhs = -lhs;
    ulong64 int1Hi = ulong64(lhs) >> 32;
    ulong64 int1Lo = ulong64(lhs & 0xFFFFFFFF);

    if (rhs < 0)
      rhs = -rhs;
    ulong64 int2Hi = ulong64(rhs) >> 32;
    ulong64 int2Lo = ulong64(rhs & 0xFFFFFFFF);

    //nb: see comments in clipper.pas
    ulong64 a = int1Hi * int2Hi;
    ulong64 b = int1Lo * int2Lo;
    ulong64 c = int1Hi * int2Lo + int1Lo * int2Hi;

    Int128 tmp;
    tmp.hi = long64(a + (c >> 32));
    tmp.lo = long64(c << 32);
    tmp.lo += long64(b);
    if (tmp.lo < b)
      tmp.hi++;
    if (negate)
      tmp = -tmp;
    return tmp;
  };
#endif

//------------------------------------------------------------------------------
// Miscellaneous global functions
//------------------------------------------------------------------------------

  bool Orientation(const Path &poly)
  {
    return Area(poly) >= 0;
  }
//------------------------------------------------------------------------------

  double Area(const Path &poly)
  {
    int size = (int) poly.size();
    if (size < 3)
      return 0;

    double a = 0;
    for (int i = 0, j = size - 1; i < size; ++i)
    {
      a += ((double) poly[j].X + poly[i].X) * ((double) poly[j].Y - poly[i].Y);
      j = i;
    }
    return -a * 0.5;
  }
//------------------------------------------------------------------------------

  double Area(const OutPt *op)
  {
    const OutPt *startOp = op;
    if (!op)
      return 0;
    double a = 0;
    do
    {
      a += (double) (op->Prev->Pt.X + op->Pt.X) * (double) (op->Prev->Pt.Y - op->Pt.Y);
      op = op->Next;
    } while (op != startOp);
    return a * 0.5;
  }
//------------------------------------------------------------------------------

  double Area(const OutRec &outRec)
  {
    return Area(outRec.Pts);
  }
//------------------------------------------------------------------------------

  bool PointIsVertex(const IntPoint &Pt, OutPt *pp)
  {
    OutPt *pp2 = pp;
    do
    {
      if (pp2->Pt == Pt)
        return true;
      pp2 = pp2->Next;
    } while (pp2 != pp);
    return false;
  }
//------------------------------------------------------------------------------

//See "The Point in Polygon Problem for Arbitrary Polygons" by Hormann & Agathos
//http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.5498&rep=rep1&type=pdf
  int PointInPolygon(const IntPoint &pt, const Path &path)
  {
    //returns 0 if false, +1 if true, -1 if pt ON polygon boundary
    int result = 0;
    size_t cnt = path.size();
    if (cnt < 3)
      return 0;
    IntPoint ip = path[0];
    for (size_t i = 1; i <= cnt; ++i)
    {
      IntPoint ipNext = (i == cnt ? path[0] : path[i]);
      if (ipNext.Y == pt.Y)
      {
        if ((ipNext.X == pt.X) || (ip.Y == pt.Y &&
                                   ((ipNext.X > pt.X) == (ip.X < pt.X))))
          return -1;
      }
      if ((ip.Y < pt.Y) != (ipNext.Y < pt.Y))
      {
        if (ip.X >= pt.X)
        {
          if (ipNext.X > pt.X)
            result = 1 - result;
          else
          {
            double d = (double) (ip.X - pt.X) * (ipNext.Y - pt.Y) -
                       (double) (ipNext.X - pt.X) * (ip.Y - pt.Y);
            if (!d)
              return -1;
            if ((d > 0) == (ipNext.Y > ip.Y))
              result = 1 - result;
          }
        } else
        {
          if (ipNext.X > pt.X)
          {
            double d = (double) (ip.X - pt.X) * (ipNext.Y - pt.Y) -
                       (double) (ipNext.X - pt.X) * (ip.Y - pt.Y);
            if (!d)
              return -1;
            if ((d > 0) == (ipNext.Y > ip.Y))
              result = 1 - result;
          }
        }
      }
      ip = ipNext;
    }
    return result;
  }
//------------------------------------------------------------------------------

  int PointInPolygon(const IntPoint &pt, OutPt *op)
  {
    //returns 0 if false, +1 if true, -1 if pt ON polygon boundary
    int result = 0;
    OutPt *startOp = op;
    for (;;)
    {
      if (op->Next->Pt.Y == pt.Y)
      {
        if ((op->Next->Pt.X == pt.X) || (op->Pt.Y == pt.Y &&
                                         ((op->Next->Pt.X > pt.X) == (op->Pt.X < pt.X))))
          return -1;
      }
      if ((op->Pt.Y < pt.Y) != (op->Next->Pt.Y < pt.Y))
      {
        if (op->Pt.X >= pt.X)
        {
          if (op->Next->Pt.X > pt.X)
            result = 1 - result;
          else
          {
            double d = (double) (op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) -
                       (double) (op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);
            if (!d)
              return -1;
            if ((d > 0) == (op->Next->Pt.Y > op->Pt.Y))
              result = 1 - result;
          }
        } else
        {
          if (op->Next->Pt.X > pt.X)
          {
            double d = (double) (op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) -
                       (double) (op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);
            if (!d)
              return -1;
            if ((d > 0) == (op->Next->Pt.Y > op->Pt.Y))
              result = 1 - result;
          }
        }
      }
      op = op->Next;
      if (startOp == op)
        break;
    }
    return result;
  }
//------------------------------------------------------------------------------

  bool Poly2ContainsPoly1(OutPt *OutPt1, OutPt *OutPt2)
  {
    OutPt *op = OutPt1;
    do
    {
      //nb: PointInPolygon returns 0 if false, +1 if true, -1 if pt on polygon
      int res = PointInPolygon(op->Pt, OutPt2);
      if (res >= 0)
        return res > 0;
      op = op->Next;
    } while (op != OutPt1);
    return true;
  }
//----------------------------------------------------------------------

  bool SlopesEqual(const TEdge &e1, const TEdge &e2, bool UseFullInt64Range)
  {
#ifndef use_int32
    if (UseFullInt64Range)
      return Int128Mul(e1.Top.Y - e1.Bot.Y, e2.Top.X - e2.Bot.X) ==
             Int128Mul(e1.Top.X - e1.Bot.X, e2.Top.Y - e2.Bot.Y);
    else
#endif
      return (e1.Top.Y - e1.Bot.Y) * (e2.Top.X - e2.Bot.X) ==
             (e1.Top.X - e1.Bot.X) * (e2.Top.Y - e2.Bot.Y);
  }
//------------------------------------------------------------------------------

  bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
                   const IntPoint pt3, bool UseFullInt64Range)
  {
#ifndef use_int32
    if (UseFullInt64Range)
      return Int128Mul(pt1.Y - pt2.Y, pt2.X - pt3.X) == Int128Mul(pt1.X - pt2.X, pt2.Y - pt3.Y);
    else
#endif
      return (pt1.Y - pt2.Y) * (pt2.X - pt3.X) == (pt1.X - pt2.X) * (pt2.Y - pt3.Y);
  }
//------------------------------------------------------------------------------

  bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
                   const IntPoint pt3, const IntPoint pt4, bool UseFullInt64Range)
  {
#ifndef use_int32
    if (UseFullInt64Range)
      return Int128Mul(pt1.Y - pt2.Y, pt3.X - pt4.X) == Int128Mul(pt1.X - pt2.X, pt3.Y - pt4.Y);
    else
#endif
      return (pt1.Y - pt2.Y) * (pt3.X - pt4.X) == (pt1.X - pt2.X) * (pt3.Y - pt4.Y);
  }
//------------------------------------------------------------------------------

  inline bool IsHorizontal(TEdge &e)
  {
    return e.Dx == HORIZONTAL;
  }
//------------------------------------------------------------------------------

  inline double GetDx(const IntPoint pt1, const IntPoint pt2)
  {
    return (pt1.Y == pt2.Y) ?
           HORIZONTAL : (double) (pt2.X - pt1.X) / (pt2.Y - pt1.Y);
  }
//---------------------------------------------------------------------------

  inline void SetDx(TEdge &e)
  {
    cInt dy = (e.Top.Y - e.Bot.Y);
    if (dy == 0)
      e.Dx = HORIZONTAL;
    else
      e.Dx = (double) (e.Top.X - e.Bot.X) / dy;
  }
//---------------------------------------------------------------------------

  inline void SwapSides(TEdge &Edge1, TEdge &Edge2)
  {
    EdgeSide Side = Edge1.Side;
    Edge1.Side = Edge2.Side;
    Edge2.Side = Side;
  }
//------------------------------------------------------------------------------

  inline void SwapPolyIndexes(TEdge &Edge1, TEdge &Edge2)
  {
    int OutIdx = Edge1.OutIdx;
    Edge1.OutIdx = Edge2.OutIdx;
    Edge2.OutIdx = OutIdx;
  }
//------------------------------------------------------------------------------

  inline cInt TopX(TEdge &edge, const cInt currentY)
  {
    return (currentY == edge.Top.Y) ?
           edge.Top.X : edge.Bot.X + Round(edge.Dx * (currentY - edge.Bot.Y));
  }
//------------------------------------------------------------------------------

  void IntersectPoint(TEdge &Edge1, TEdge &Edge2, IntPoint &ip)
  {
#ifdef use_xyz
    ip.Z = 0;
#endif

    double b1, b2;
    if (Edge1.Dx == Edge2.Dx)
    {
      ip.Y = Edge1.Curr.Y;
      ip.X = TopX(Edge1, ip.Y);
      return;
    } else if (Edge1.Dx == 0)
    {
      ip.X = Edge1.Bot.X;
      if (IsHorizontal(Edge2))
        ip.Y = Edge2.Bot.Y;
      else
      {
        b2 = Edge2.Bot.Y - (Edge2.Bot.X / Edge2.Dx);
        ip.Y = Round(ip.X / Edge2.Dx + b2);
      }
    } else if (Edge2.Dx == 0)
    {
      ip.X = Edge2.Bot.X;
      if (IsHorizontal(Edge1))
        ip.Y = Edge1.Bot.Y;
      else
      {
        b1 = Edge1.Bot.Y - (Edge1.Bot.X / Edge1.Dx);
        ip.Y = Round(ip.X / Edge1.Dx + b1);
      }
    } else
    {
      b1 = Edge1.Bot.X - Edge1.Bot.Y * Edge1.Dx;
      b2 = Edge2.Bot.X - Edge2.Bot.Y * Edge2.Dx;
      double q = (b2 - b1) / (Edge1.Dx - Edge2.Dx);
      ip.Y = Round(q);
      if (std::fabs(Edge1.Dx) < std::fabs(Edge2.Dx))
        ip.X = Round(Edge1.Dx * q + b1);
      else
        ip.X = Round(Edge2.Dx * q + b2);
    }

    if (ip.Y < Edge1.Top.Y || ip.Y < Edge2.Top.Y)
    {
      if (Edge1.Top.Y > Edge2.Top.Y)
        ip.Y = Edge1.Top.Y;
      else
        ip.Y = Edge2.Top.Y;
      if (std::fabs(Edge1.Dx) < std::fabs(Edge2.Dx))
        ip.X = TopX(Edge1, ip.Y);
      else
        ip.X = TopX(Edge2, ip.Y);
    }
    //finally, don't allow 'ip' to be BELOW curr.Y (ie bottom of scanbeam) ...
    if (ip.Y > Edge1.Curr.Y)
    {
      ip.Y = Edge1.Curr.Y;
      //use the more vertical edge to derive X ...
      if (std::fabs(Edge1.Dx) > std::fabs(Edge2.Dx))
        ip.X = TopX(Edge2, ip.Y);
      else
        ip.X = TopX(Edge1, ip.Y);
    }
  }
//------------------------------------------------------------------------------

  void ReversePolyPtLinks(OutPt *pp)
  {
    if (!pp)
      return;
    OutPt *pp1, *pp2;
    pp1 = pp;
    do
    {
      pp2 = pp1->Next;
      pp1->Next = pp1->Prev;
      pp1->Prev = pp2;
      pp1 = pp2;
    } while (pp1 != pp);
  }
//------------------------------------------------------------------------------

  void DisposeOutPts(OutPt *&pp)
  {
    if (pp == 0)
      return;
    pp->Prev->Next = 0;
    while (pp)
    {
      OutPt *tmpPp = pp;
      pp = pp->Next;
      delete tmpPp;
    }
  }
//------------------------------------------------------------------------------

  inline void InitEdge(TEdge *e, TEdge *eNext, TEdge *ePrev, const IntPoint &Pt)
  {
    std::memset(e, 0, sizeof(TEdge));
    e->Next = eNext;
    e->Prev = ePrev;
    e->Curr = Pt;
    e->OutIdx = Unassigned;
  }
//------------------------------------------------------------------------------

  void InitEdge2(TEdge &e, PolyType Pt)
  {
    if (e.Curr.Y >= e.Next->Curr.Y)
    {
      e.Bot = e.Curr;
      e.Top = e.Next->Curr;
    } else
    {
      e.Top = e.Curr;
      e.Bot = e.Next->Curr;
    }
    SetDx(e);
    e.PolyTyp = Pt;
  }
//------------------------------------------------------------------------------

  TEdge *RemoveEdge(TEdge *e)
  {
    //removes e from double_linked_list (but without removing from memory)
    e->Prev->Next = e->Next;
    e->Next->Prev = e->Prev;
    TEdge *result = e->Next;
    e->Prev = 0; //flag as removed (see ClipperBase.Clear)
    return result;
  }
//------------------------------------------------------------------------------

  inline void ReverseHorizontal(TEdge &e)
  {
    //swap horizontal edges' Top and Bottom x's so they follow the natural
    //progression of the bounds - ie so their xbots will align with the
    //adjoining lower edge. [Helpful in the ProcessHorizontal() method.]
    std::swap(e.Top.X, e.Bot.X);
#ifdef use_xyz
    std::swap(e.Top.Z, e.Bot.Z);
#endif
  }
//------------------------------------------------------------------------------

  void SwapPoints(IntPoint &pt1, IntPoint &pt2)
  {
    IntPoint tmp = pt1;
    pt1 = pt2;
    pt2 = tmp;
  }
//------------------------------------------------------------------------------

  bool GetOverlapSegment(IntPoint pt1a, IntPoint pt1b, IntPoint pt2a,
                         IntPoint pt2b, IntPoint &pt1, IntPoint &pt2)
  {
    //precondition: segments are Collinear.
    if (Abs(pt1a.X - pt1b.X) > Abs(pt1a.Y - pt1b.Y))
    {
      if (pt1a.X > pt1b.X)
        SwapPoints(pt1a, pt1b);
      if (pt2a.X > pt2b.X)
        SwapPoints(pt2a, pt2b);
      if (pt1a.X > pt2a.X)
        pt1 = pt1a;
      else
        pt1 = pt2a;
      if (pt1b.X < pt2b.X)
        pt2 = pt1b;
      else
        pt2 = pt2b;
      return pt1.X < pt2.X;
    } else
    {
      if (pt1a.Y < pt1b.Y)
        SwapPoints(pt1a, pt1b);
      if (pt2a.Y < pt2b.Y)
        SwapPoints(pt2a, pt2b);
      if (pt1a.Y < pt2a.Y)
        pt1 = pt1a;
      else
        pt1 = pt2a;
      if (pt1b.Y > pt2b.Y)
        pt2 = pt1b;
      else
        pt2 = pt2b;
      return pt1.Y > pt2.Y;
    }
  }
//------------------------------------------------------------------------------

  bool FirstIsBottomPt(const OutPt *btmPt1, const OutPt *btmPt2)
  {
    OutPt *p = btmPt1->Prev;
    while ((p->Pt == btmPt1->Pt) && (p != btmPt1))
      p = p->Prev;
    double dx1p = std::fabs(GetDx(btmPt1->Pt, p->Pt));
    p = btmPt1->Next;
    while ((p->Pt == btmPt1->Pt) && (p != btmPt1))
      p = p->Next;
    double dx1n = std::fabs(GetDx(btmPt1->Pt, p->Pt));

    p = btmPt2->Prev;
    while ((p->Pt == btmPt2->Pt) && (p != btmPt2))
      p = p->Prev;
    double dx2p = std::fabs(GetDx(btmPt2->Pt, p->Pt));
    p = btmPt2->Next;
    while ((p->Pt == btmPt2->Pt) && (p != btmPt2))
      p = p->Next;
    double dx2n = std::fabs(GetDx(btmPt2->Pt, p->Pt));

    if (std::max(dx1p, dx1n) == std::max(dx2p, dx2n) &&
        std::min(dx1p, dx1n) == std::min(dx2p, dx2n))
      return Area(btmPt1) > 0; //if otherwise identical use orientation
    else
      return (dx1p >= dx2p && dx1p >= dx2n) || (dx1n >= dx2p && dx1n >= dx2n);
  }
//------------------------------------------------------------------------------

  OutPt *GetBottomPt(OutPt *pp)
  {
    OutPt *dups = 0;
    OutPt *p = pp->Next;
    while (p != pp)
    {
      if (p->Pt.Y > pp->Pt.Y)
      {
        pp = p;
        dups = 0;
      } else if (p->Pt.Y == pp->Pt.Y && p->Pt.X <= pp->Pt.X)
      {
        if (p->Pt.X < pp->Pt.X)
        {
          dups = 0;
          pp = p;
        } else
        {
          if (p->Next != pp && p->Prev != pp)
            dups = p;
        }
      }
      p = p->Next;
    }
    if (dups)
    {
      //there appears to be at least 2 vertices at BottomPt so ...
      while (dups != p)
      {
        if (!FirstIsBottomPt(p, dups))
          pp = dups;
        dups = dups->Next;
        while (dups->Pt != pp->Pt)
          dups = dups->Next;
      }
    }
    return pp;
  }
//------------------------------------------------------------------------------

  bool Pt2IsBetweenPt1AndPt3(const IntPoint pt1,
                             const IntPoint pt2, const IntPoint pt3)
  {
    if ((pt1 == pt3) || (pt1 == pt2) || (pt3 == pt2))
      return false;
    else if (pt1.X != pt3.X)
      return (pt2.X > pt1.X) == (pt2.X < pt3.X);
    else
      return (pt2.Y > pt1.Y) == (pt2.Y < pt3.Y);
  }
//------------------------------------------------------------------------------

  bool HorzSegmentsOverlap(cInt seg1a, cInt seg1b, cInt seg2a, cInt seg2b)
  {
    if (seg1a > seg1b)
      std::swap(seg1a, seg1b);
    if (seg2a > seg2b)
      std::swap(seg2a, seg2b);
    return (seg1a < seg2b) && (seg2a < seg1b);
  }

//------------------------------------------------------------------------------
// ClipperBase class methods ...
//------------------------------------------------------------------------------

  ClipperBase::ClipperBase() //constructor
  {
    m_CurrentLM = m_MinimaList.begin(); //begin() == end() here
    m_UseFullRange = false;
  }
//------------------------------------------------------------------------------

  ClipperBase::~ClipperBase() //destructor
  {
    Clear();
  }
//------------------------------------------------------------------------------

  void RangeTest(const IntPoint &Pt, bool &useFullRange)
  {
    if (useFullRange)
    {
      if (Pt.X > hiRange || Pt.Y > hiRange || -Pt.X > hiRange || -Pt.Y > hiRange)
        throw clipperException("Coordinate outside allowed range");
    } else if (Pt.X > loRange || Pt.Y > loRange || -Pt.X > loRange || -Pt.Y > loRange)
    {
      useFullRange = true;
      RangeTest(Pt, useFullRange);
    }
  }
//------------------------------------------------------------------------------

  TEdge *FindNextLocMin(TEdge *E)
  {
    for (;;)
    {
      while (E->Bot != E->Prev->Bot || E->Curr == E->Top)
        E = E->Next;
      if (!IsHorizontal(*E) && !IsHorizontal(*E->Prev))
        break;
      while (IsHorizontal(*E->Prev))
        E = E->Prev;
      TEdge *E2 = E;
      while (IsHorizontal(*E))
        E = E->Next;
      if (E->Top.Y == E->Prev->Bot.Y)
        continue; //ie just an intermediate horz.
      if (E2->Prev->Bot.X < E->Bot.X)
        E = E2;
      break;
    }
    return E;
  }
//------------------------------------------------------------------------------

  TEdge *ClipperBase::ProcessBound(TEdge *E, bool NextIsForward)
  {
    TEdge *Result = E;
    TEdge *Horz = 0;

    if (E->OutIdx == Skip)
    {
      //if edges still remain in the current bound beyond the skip edge then
      //create another LocMin and call ProcessBound once more
      if (NextIsForward)
      {
        while (E->Top.Y == E->Next->Bot.Y)
          E = E->Next;
        //don't include top horizontals when parsing a bound a second time,
        //they will be contained in the opposite bound ...
        while (E != Result && IsHorizontal(*E))
          E = E->Prev;
      } else
      {
        while (E->Top.Y == E->Prev->Bot.Y)
          E = E->Prev;
        while (E != Result && IsHorizontal(*E))
          E = E->Next;
      }

      if (E == Result)
      {
        if (NextIsForward)
          Result = E->Next;
        else
          Result = E->Prev;
      } else
      {
        //there are more edges in the bound beyond result starting with E
        if (NextIsForward)
          E = Result->Next;
        else
          E = Result->Prev;
        MinimaList::value_type locMin;
        locMin.Y = E->Bot.Y;
        locMin.LeftBound = 0;
        locMin.RightBound = E;
        E->WindDelta = 0;
        Result = ProcessBound(E, NextIsForward);
        m_MinimaList.push_back(locMin);
      }
      return Result;
    }

    TEdge *EStart;

    if (IsHorizontal(*E))
    {
      //We need to be careful with open paths because this may not be a
      //true local minima (ie E may be following a skip edge).
      //Also, consecutive horz. edges may start heading left before going right.
      if (NextIsForward)
        EStart = E->Prev;
      else
        EStart = E->Next;
      if (IsHorizontal(*EStart)) //ie an adjoining horizontal skip edge
      {
        if (EStart->Bot.X != E->Bot.X && EStart->Top.X != E->Bot.X)
          ReverseHorizontal(*E);
      } else if (EStart->Bot.X != E->Bot.X)
        ReverseHorizontal(*E);
    }

    EStart = E;
    if (NextIsForward)
    {
      while (Result->Top.Y == Result->Next->Bot.Y && Result->Next->OutIdx != Skip)
        Result = Result->Next;
      if (IsHorizontal(*Result) && Result->Next->OutIdx != Skip)
      {
        //nb: at the top of a bound, horizontals are added to the bound
        //only when the preceding edge attaches to the horizontal's left vertex
        //unless a Skip edge is encountered when that becomes the top divide
        Horz = Result;
        while (IsHorizontal(*Horz->Prev))
          Horz = Horz->Prev;
        if (Horz->Prev->Top.X > Result->Next->Top.X)
          Result = Horz->Prev;
      }
      while (E != Result)
      {
        E->NextInLML = E->Next;
        if (IsHorizontal(*E) && E != EStart &&
            E->Bot.X != E->Prev->Top.X)
          ReverseHorizontal(*E);
        E = E->Next;
      }
      if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Prev->Top.X)
        ReverseHorizontal(*E);
      Result = Result->Next; //move to the edge just beyond current bound
    } else
    {
      while (Result->Top.Y == Result->Prev->Bot.Y && Result->Prev->OutIdx != Skip)
        Result = Result->Prev;
      if (IsHorizontal(*Result) && Result->Prev->OutIdx != Skip)
      {
        Horz = Result;
        while (IsHorizontal(*Horz->Next))
          Horz = Horz->Next;
        if (Horz->Next->Top.X == Result->Prev->Top.X ||
            Horz->Next->Top.X > Result->Prev->Top.X)
          Result = Horz->Next;
      }

      while (E != Result)
      {
        E->NextInLML = E->Prev;
        if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Next->Top.X)
          ReverseHorizontal(*E);
        E = E->Prev;
      }
      if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Next->Top.X)
        ReverseHorizontal(*E);
      Result = Result->Prev; //move to the edge just beyond current bound
    }

    return Result;
  }
//------------------------------------------------------------------------------

  bool ClipperBase::AddPath(const Path &pg, PolyType PolyTyp, bool Closed)
  {
#ifdef use_lines
    if (!Closed && PolyTyp == ptClip)
      throw clipperException("AddPath: Open paths must be subject.");
#else
                                                                                                                            if (!Closed)
    throw clipperException("AddPath: Open paths have been disabled.");
#endif

    int highI = (int) pg.size() - 1;
    if (Closed)
      while (highI > 0 && (pg[highI] == pg[0]))
        --highI;
    while (highI > 0 && (pg[highI] == pg[highI - 1]))
      --highI;
    if ((Closed && highI < 2) || (!Closed && highI < 1))
      return false;

    //create a new edge array ...
    TEdge *edges = new TEdge[highI + 1];

    bool IsFlat = true;
    //1. Basic (first) edge initialization ...
    try
    {
      edges[1].Curr = pg[1];
      RangeTest(pg[0], m_UseFullRange);
      RangeTest(pg[highI], m_UseFullRange);
      InitEdge(&edges[0], &edges[1], &edges[highI], pg[0]);
      InitEdge(&edges[highI], &edges[0], &edges[highI - 1], pg[highI]);
      for (int i = highI - 1; i >= 1; --i)
      {
        RangeTest(pg[i], m_UseFullRange);
        InitEdge(&edges[i], &edges[i + 1], &edges[i - 1], pg[i]);
      }
    }
    catch (...)
    {
      delete[] edges;
      throw; //range test fails
    }
    TEdge *eStart = &edges[0];

    //2. Remove duplicate vertices, and (when closed) collinear edges ...
    TEdge *E = eStart, *eLoopStop = eStart;
    for (;;)
    {
      //nb: allows matching start and end points when not Closed ...
      if (E->Curr == E->Next->Curr && (Closed || E->Next != eStart))
      {
        if (E == E->Next)
          break;
        if (E == eStart)
          eStart = E->Next;
        E = RemoveEdge(E);
        eLoopStop = E;
        continue;
      }
      if (E->Prev == E->Next)
        break; //only two vertices
      else if (Closed &&
               SlopesEqual(E->Prev->Curr, E->Curr, E->Next->Curr, m_UseFullRange) &&
               (!m_PreserveCollinear ||
                !Pt2IsBetweenPt1AndPt3(E->Prev->Curr, E->Curr, E->Next->Curr)))
      {
        //Collinear edges are allowed for open paths but in closed paths
        //the default is to merge adjacent collinear edges into a single edge.
        //However, if the PreserveCollinear property is enabled, only overlapping
        //collinear edges (ie spikes) will be removed from closed paths.
        if (E == eStart)
          eStart = E->Next;
        E = RemoveEdge(E);
        E = E->Prev;
        eLoopStop = E;
        continue;
      }
      E = E->Next;
      if ((E == eLoopStop) || (!Closed && E->Next == eStart))
        break;
    }

    if ((!Closed && (E == E->Next)) || (Closed && (E->Prev == E->Next)))
    {
      delete[] edges;
      return false;
    }

    if (!Closed)
    {
      m_HasOpenPaths = true;
      eStart->Prev->OutIdx = Skip;
    }

    //3. Do second stage of edge initialization ...
    E = eStart;
    do
    {
      InitEdge2(*E, PolyTyp);
      E = E->Next;
      if (IsFlat && E->Curr.Y != eStart->Curr.Y)
        IsFlat = false;
    } while (E != eStart);

    //4. Finally, add edge bounds to LocalMinima list ...

    //Totally flat paths must be handled differently when adding them
    //to LocalMinima list to avoid endless loops etc ...
    if (IsFlat)
    {
      if (Closed)
      {
        delete[] edges;
        return false;
      }
      E->Prev->OutIdx = Skip;
      MinimaList::value_type locMin;
      locMin.Y = E->Bot.Y;
      locMin.LeftBound = 0;
      locMin.RightBound = E;
      locMin.RightBound->Side = esRight;
      locMin.RightBound->WindDelta = 0;
      for (;;)
      {
        if (E->Bot.X != E->Prev->Top.X)
          ReverseHorizontal(*E);
        if (E->Next->OutIdx == Skip)
          break;
        E->NextInLML = E->Next;
        E = E->Next;
      }
      m_MinimaList.push_back(locMin);
      m_edges.push_back(edges);
      return true;
    }

    m_edges.push_back(edges);
    bool leftBoundIsForward;
    TEdge *EMin = 0;

    //workaround to avoid an endless loop in the while loop below when
    //open paths have matching start and end points ...
    if (E->Prev->Bot == E->Prev->Top)
      E = E->Next;

    for (;;)
    {
      E = FindNextLocMin(E);
      if (E == EMin)
        break;
      else if (!EMin)
        EMin = E;

      //E and E.Prev now share a local minima (left aligned if horizontal).
      //Compare their slopes to find which starts which bound ...
      MinimaList::value_type locMin;
      locMin.Y = E->Bot.Y;
      if (E->Dx < E->Prev->Dx)
      {
        locMin.LeftBound = E->Prev;
        locMin.RightBound = E;
        leftBoundIsForward = false; //Q.nextInLML = Q.prev
      } else
      {
        locMin.LeftBound = E;
        locMin.RightBound = E->Prev;
        leftBoundIsForward = true; //Q.nextInLML = Q.next
      }

      if (!Closed)
        locMin.LeftBound->WindDelta = 0;
      else if (locMin.LeftBound->Next == locMin.RightBound)
        locMin.LeftBound->WindDelta = -1;
      else
        locMin.LeftBound->WindDelta = 1;
      locMin.RightBound->WindDelta = -locMin.LeftBound->WindDelta;

      E = ProcessBound(locMin.LeftBound, leftBoundIsForward);
      if (E->OutIdx == Skip)
        E = ProcessBound(E, leftBoundIsForward);

      TEdge *E2 = ProcessBound(locMin.RightBound, !leftBoundIsForward);
      if (E2->OutIdx == Skip)
        E2 = ProcessBound(E2, !leftBoundIsForward);

      if (locMin.LeftBound->OutIdx == Skip)
        locMin.LeftBound = 0;
      else if (locMin.RightBound->OutIdx == Skip)
        locMin.RightBound = 0;
      m_MinimaList.push_back(locMin);
      if (!leftBoundIsForward)
        E = E2;
    }
    return true;
  }
//------------------------------------------------------------------------------

  bool ClipperBase::AddPaths(const Paths &ppg, PolyType PolyTyp, bool Closed)
  {
    bool result = false;
    for (Paths::size_type i = 0; i < ppg.size(); ++i)
      if (AddPath(ppg[i], PolyTyp, Closed))
        result = true;
    return result;
  }
//------------------------------------------------------------------------------

  void ClipperBase::Clear()
  {
    DisposeLocalMinimaList();
    for (EdgeList::size_type i = 0; i < m_edges.size(); ++i)
    {
      TEdge *edges = m_edges[i];
      delete[] edges;
    }
    m_edges.clear();
    m_UseFullRange = false;
    m_HasOpenPaths = false;
  }
//------------------------------------------------------------------------------

  void ClipperBase::Reset()
  {
    m_CurrentLM = m_MinimaList.begin();
    if (m_CurrentLM == m_MinimaList.end())
      return; //ie nothing to process
    std::sort(m_MinimaList.begin(), m_MinimaList.end(), LocMinSorter());

    m_Scanbeam = ScanbeamList(); //clears/resets priority_queue
    //reset all edges ...
    for (MinimaList::iterator lm = m_MinimaList.begin(); lm != m_MinimaList.end(); ++lm)
    {
      InsertScanbeam(lm->Y);
      TEdge *e = lm->LeftBound;
      if (e)
      {
        e->Curr = e->Bot;
        e->Side = esLeft;
        e->OutIdx = Unassigned;
      }

      e = lm->RightBound;
      if (e)
      {
        e->Curr = e->Bot;
        e->Side = esRight;
        e->OutIdx = Unassigned;
      }
    }
    m_ActiveEdges = 0;
    m_CurrentLM = m_MinimaList.begin();
  }
//------------------------------------------------------------------------------

  void ClipperBase::DisposeLocalMinimaList()
  {
    m_MinimaList.clear();
    m_CurrentLM = m_MinimaList.begin();
  }
//------------------------------------------------------------------------------

  bool ClipperBase::PopLocalMinima(cInt Y, const LocalMinimum *&locMin)
  {
    if (m_CurrentLM == m_MinimaList.end() || (*m_CurrentLM).Y != Y)
      return false;
    locMin = &(*m_CurrentLM);
    ++m_CurrentLM;
    return true;
  }
//------------------------------------------------------------------------------

  IntRect ClipperBase::GetBounds()
  {
    IntRect result;
    MinimaList::iterator lm = m_MinimaList.begin();
    if (lm == m_MinimaList.end())
    {
      result.left = result.top = result.right = result.bottom = 0;
      return result;
    }
    result.left = lm->LeftBound->Bot.X;
    result.top = lm->LeftBound->Bot.Y;
    result.right = lm->LeftBound->Bot.X;
    result.bottom = lm->LeftBound->Bot.Y;
    while (lm != m_MinimaList.end())
    {
      //todo - needs fixing for open paths
      result.bottom = std::max(result.bottom, lm->LeftBound->Bot.Y);
      TEdge *e = lm->LeftBound;
      for (;;)
      {
        TEdge *bottomE = e;
        while (e->NextInLML)
        {
          if (e->Bot.X < result.left)
            result.left = e->Bot.X;
          if (e->Bot.X > result.right)
            result.right = e->Bot.X;
          e = e->NextInLML;
        }
        result.left = std::min(result.left, e->Bot.X);
        result.right = std::max(result.right, e->Bot.X);
        result.left = std::min(result.left, e->Top.X);
        result.right = std::max(result.right, e->Top.X);
        result.top = std::min(result.top, e->Top.Y);
        if (bottomE == lm->LeftBound)
          e = lm->RightBound;
        else
          break;
      }
      ++lm;
    }
    return result;
  }
//------------------------------------------------------------------------------

  void ClipperBase::InsertScanbeam(const cInt Y)
  {
    m_Scanbeam.push(Y);
  }
//------------------------------------------------------------------------------

  bool ClipperBase::PopScanbeam(cInt &Y)
  {
    if (m_Scanbeam.empty())
      return false;
    Y = m_Scanbeam.top();
    m_Scanbeam.pop();
    while (!m_Scanbeam.empty() && Y == m_Scanbeam.top())
    {
      m_Scanbeam.pop();
    } // Pop duplicates.
    return true;
  }
//------------------------------------------------------------------------------

  void ClipperBase::DisposeAllOutRecs()
  {
    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
      DisposeOutRec(i);
    m_PolyOuts.clear();
  }
//------------------------------------------------------------------------------

  void ClipperBase::DisposeOutRec(PolyOutList::size_type index)
  {
    OutRec *outRec = m_PolyOuts[index];
    if (outRec->Pts)
      DisposeOutPts(outRec->Pts);
    delete outRec;
    m_PolyOuts[index] = 0;
  }
//------------------------------------------------------------------------------

  void ClipperBase::DeleteFromAEL(TEdge *e)
  {
    TEdge *AelPrev = e->PrevInAEL;
    TEdge *AelNext = e->NextInAEL;
    if (!AelPrev && !AelNext && (e != m_ActiveEdges))
      return; //already deleted
    if (AelPrev)
      AelPrev->NextInAEL = AelNext;
    else
      m_ActiveEdges = AelNext;
    if (AelNext)
      AelNext->PrevInAEL = AelPrev;
    e->NextInAEL = 0;
    e->PrevInAEL = 0;
  }
//------------------------------------------------------------------------------

  OutRec *ClipperBase::CreateOutRec()
  {
    OutRec *result = new OutRec;
    result->IsHole = false;
    result->IsOpen = false;
    result->FirstLeft = 0;
    result->Pts = 0;
    result->BottomPt = 0;
    result->PolyNd = 0;
    m_PolyOuts.push_back(result);
    result->Idx = (int) m_PolyOuts.size() - 1;
    return result;
  }
//------------------------------------------------------------------------------

  void ClipperBase::SwapPositionsInAEL(TEdge *Edge1, TEdge *Edge2)
  {
    //check that one or other edge hasn't already been removed from AEL ...
    if (Edge1->NextInAEL == Edge1->PrevInAEL ||
        Edge2->NextInAEL == Edge2->PrevInAEL)
      return;

    if (Edge1->NextInAEL == Edge2)
    {
      TEdge *Next = Edge2->NextInAEL;
      if (Next)
        Next->PrevInAEL = Edge1;
      TEdge *Prev = Edge1->PrevInAEL;
      if (Prev)
        Prev->NextInAEL = Edge2;
      Edge2->PrevInAEL = Prev;
      Edge2->NextInAEL = Edge1;
      Edge1->PrevInAEL = Edge2;
      Edge1->NextInAEL = Next;
    } else if (Edge2->NextInAEL == Edge1)
    {
      TEdge *Next = Edge1->NextInAEL;
      if (Next)
        Next->PrevInAEL = Edge2;
      TEdge *Prev = Edge2->PrevInAEL;
      if (Prev)
        Prev->NextInAEL = Edge1;
      Edge1->PrevInAEL = Prev;
      Edge1->NextInAEL = Edge2;
      Edge2->PrevInAEL = Edge1;
      Edge2->NextInAEL = Next;
    } else
    {
      TEdge *Next = Edge1->NextInAEL;
      TEdge *Prev = Edge1->PrevInAEL;
      Edge1->NextInAEL = Edge2->NextInAEL;
      if (Edge1->NextInAEL)
        Edge1->NextInAEL->PrevInAEL = Edge1;
      Edge1->PrevInAEL = Edge2->PrevInAEL;
      if (Edge1->PrevInAEL)
        Edge1->PrevInAEL->NextInAEL = Edge1;
      Edge2->NextInAEL = Next;
      if (Edge2->NextInAEL)
        Edge2->NextInAEL->PrevInAEL = Edge2;
      Edge2->PrevInAEL = Prev;
      if (Edge2->PrevInAEL)
        Edge2->PrevInAEL->NextInAEL = Edge2;
    }

    if (!Edge1->PrevInAEL)
      m_ActiveEdges = Edge1;
    else if (!Edge2->PrevInAEL)
      m_ActiveEdges = Edge2;
  }
//------------------------------------------------------------------------------

  void ClipperBase::UpdateEdgeIntoAEL(TEdge *&e)
  {
    if (!e->NextInLML)
      throw clipperException("UpdateEdgeIntoAEL: invalid call");

    e->NextInLML->OutIdx = e->OutIdx;
    TEdge *AelPrev = e->PrevInAEL;
    TEdge *AelNext = e->NextInAEL;
    if (AelPrev)
      AelPrev->NextInAEL = e->NextInLML;
    else
      m_ActiveEdges = e->NextInLML;
    if (AelNext)
      AelNext->PrevInAEL = e->NextInLML;
    e->NextInLML->Side = e->Side;
    e->NextInLML->WindDelta = e->WindDelta;
    e->NextInLML->WindCnt = e->WindCnt;
    e->NextInLML->WindCnt2 = e->WindCnt2;
    e = e->NextInLML;
    e->Curr = e->Bot;
    e->PrevInAEL = AelPrev;
    e->NextInAEL = AelNext;
    if (!IsHorizontal(*e))
      InsertScanbeam(e->Top.Y);
  }
//------------------------------------------------------------------------------

  bool ClipperBase::LocalMinimaPending()
  {
    return (m_CurrentLM != m_MinimaList.end());
  }

//------------------------------------------------------------------------------
// TClipper methods ...
//------------------------------------------------------------------------------

  Clipper::Clipper(int initOptions) : ClipperBase() //constructor
  {
    m_ExecuteLocked = false;
    m_UseFullRange = false;
    m_ReverseOutput = ((initOptions & ioReverseSolution) != 0);
    m_StrictSimple = ((initOptions & ioStrictlySimple) != 0);
    m_PreserveCollinear = ((initOptions & ioPreserveCollinear) != 0);
    m_HasOpenPaths = false;
#ifdef use_xyz
    m_ZFill = 0;
#endif
  }
//------------------------------------------------------------------------------

#ifdef use_xyz
                                                                                                                          void Clipper::ZFillFunction(ZFillCallback zFillFunc)
{
  m_ZFill = zFillFunc;
}
//------------------------------------------------------------------------------
#endif

  bool Clipper::Execute(ClipType clipType, Paths &solution, PolyFillType fillType)
  {
    return Execute(clipType, solution, fillType, fillType);
  }
//------------------------------------------------------------------------------

  bool Clipper::Execute(ClipType clipType, PolyTree &polytree, PolyFillType fillType)
  {
    return Execute(clipType, polytree, fillType, fillType);
  }
//------------------------------------------------------------------------------

  bool Clipper::Execute(ClipType clipType, Paths &solution,
                        PolyFillType subjFillType, PolyFillType clipFillType)
  {
    if (m_ExecuteLocked)
      return false;
    if (m_HasOpenPaths)
      throw clipperException("Error: PolyTree struct is needed for open path clipping.");
    m_ExecuteLocked = true;
    solution.resize(0);
    m_SubjFillType = subjFillType;
    m_ClipFillType = clipFillType;
    m_ClipType = clipType;
    m_UsingPolyTree = false;
    bool succeeded = ExecuteInternal();
    if (succeeded)
      BuildResult(solution);
    DisposeAllOutRecs();
    m_ExecuteLocked = false;
    return succeeded;
  }
//------------------------------------------------------------------------------

  bool Clipper::Execute(ClipType clipType, PolyTree &polytree,
                        PolyFillType subjFillType, PolyFillType clipFillType)
  {
    if (m_ExecuteLocked)
      return false;
    m_ExecuteLocked = true;
    m_SubjFillType = subjFillType;
    m_ClipFillType = clipFillType;
    m_ClipType = clipType;
    m_UsingPolyTree = true;
    bool succeeded = ExecuteInternal();
    if (succeeded)
      BuildResult2(polytree);
    DisposeAllOutRecs();
    m_ExecuteLocked = false;
    return succeeded;
  }
//------------------------------------------------------------------------------

  void Clipper::FixHoleLinkage(OutRec &outrec)
  {
    //skip OutRecs that (a) contain outermost polygons or
    //(b) already have the correct owner/child linkage ...
    if (!outrec.FirstLeft ||
        (outrec.IsHole != outrec.FirstLeft->IsHole &&
         outrec.FirstLeft->Pts))
      return;

    OutRec *orfl = outrec.FirstLeft;
    while (orfl && ((orfl->IsHole == outrec.IsHole) || !orfl->Pts))
      orfl = orfl->FirstLeft;
    outrec.FirstLeft = orfl;
  }
//------------------------------------------------------------------------------

  bool Clipper::ExecuteInternal()
  {
    bool succeeded = true;
    try
    {
      Reset();
      m_Maxima = MaximaList();
      m_SortedEdges = 0;

      succeeded = true;
      cInt botY, topY;
      if (!PopScanbeam(botY))
        return false;
      InsertLocalMinimaIntoAEL(botY);
      while (PopScanbeam(topY) || LocalMinimaPending())
      {
        ProcessHorizontals();
        ClearGhostJoins();
        if (!ProcessIntersections(topY))
        {
          succeeded = false;
          break;
        }
        ProcessEdgesAtTopOfScanbeam(topY);
        botY = topY;
        InsertLocalMinimaIntoAEL(botY);
      }
    }
    catch (...)
    {
      succeeded = false;
    }

    if (succeeded)
    {
      //fix orientations ...
      for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
      {
        OutRec *outRec = m_PolyOuts[i];
        if (!outRec->Pts || outRec->IsOpen)
          continue;
        if ((outRec->IsHole ^ m_ReverseOutput) == (Area(*outRec) > 0))
          ReversePolyPtLinks(outRec->Pts);
      }

      if (!m_Joins.empty())
        JoinCommonEdges();

      //unfortunately FixupOutPolygon() must be done after JoinCommonEdges()
      for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
      {
        OutRec *outRec = m_PolyOuts[i];
        if (!outRec->Pts)
          continue;
        if (outRec->IsOpen)
          FixupOutPolyline(*outRec);
        else
          FixupOutPolygon(*outRec);
      }

      if (m_StrictSimple)
        DoSimplePolygons();
    }

    ClearJoins();
    ClearGhostJoins();
    return succeeded;
  }
//------------------------------------------------------------------------------

  void Clipper::SetWindingCount(TEdge &edge)
  {
    TEdge *e = edge.PrevInAEL;
    //find the edge of the same polytype that immediately preceeds 'edge' in AEL
    while (e && ((e->PolyTyp != edge.PolyTyp) || (e->WindDelta == 0)))
      e = e->PrevInAEL;
    if (!e)
    {
      if (edge.WindDelta == 0)
      {
        PolyFillType pft = (edge.PolyTyp == ptSubject ? m_SubjFillType : m_ClipFillType);
        edge.WindCnt = (pft == pftNegative ? -1 : 1);
      } else
        edge.WindCnt = edge.WindDelta;
      edge.WindCnt2 = 0;
      e = m_ActiveEdges; //ie get ready to calc WindCnt2
    } else if (edge.WindDelta == 0 && m_ClipType != ctUnion)
    {
      edge.WindCnt = 1;
      edge.WindCnt2 = e->WindCnt2;
      e = e->NextInAEL; //ie get ready to calc WindCnt2
    } else if (IsEvenOddFillType(edge))
    {
      //EvenOdd filling ...
      if (edge.WindDelta == 0)
      {
        //are we inside a subj polygon ...
        bool Inside = true;
        TEdge *e2 = e->PrevInAEL;
        while (e2)
        {
          if (e2->PolyTyp == e->PolyTyp && e2->WindDelta != 0)
            Inside = !Inside;
          e2 = e2->PrevInAEL;
        }
        edge.WindCnt = (Inside ? 0 : 1);
      } else
      {
        edge.WindCnt = edge.WindDelta;
      }
      edge.WindCnt2 = e->WindCnt2;
      e = e->NextInAEL; //ie get ready to calc WindCnt2
    } else
    {
      //nonZero, Positive or Negative filling ...
      if (e->WindCnt * e->WindDelta < 0)
      {
        //prev edge is 'decreasing' WindCount (WC) toward zero
        //so we're outside the previous polygon ...
        if (Abs(e->WindCnt) > 1)
        {
          //outside prev poly but still inside another.
          //when reversing direction of prev poly use the same WC
          if (e->WindDelta * edge.WindDelta < 0)
            edge.WindCnt = e->WindCnt;
            //otherwise continue to 'decrease' WC ...
          else
            edge.WindCnt = e->WindCnt + edge.WindDelta;
        } else
          //now outside all polys of same polytype so set own WC ...
          edge.WindCnt = (edge.WindDelta == 0 ? 1 : edge.WindDelta);
      } else
      {
        //prev edge is 'increasing' WindCount (WC) away from zero
        //so we're inside the previous polygon ...
        if (edge.WindDelta == 0)
          edge.WindCnt = (e->WindCnt < 0 ? e->WindCnt - 1 : e->WindCnt + 1);
          //if wind direction is reversing prev then use same WC
        else if (e->WindDelta * edge.WindDelta < 0)
          edge.WindCnt = e->WindCnt;
          //otherwise add to WC ...
        else
          edge.WindCnt = e->WindCnt + edge.WindDelta;
      }
      edge.WindCnt2 = e->WindCnt2;
      e = e->NextInAEL; //ie get ready to calc WindCnt2
    }

    //update WindCnt2 ...
    if (IsEvenOddAltFillType(edge))
    {
      //EvenOdd filling ...
      while (e != &edge)
      {
        if (e->WindDelta != 0)
          edge.WindCnt2 = (edge.WindCnt2 == 0 ? 1 : 0);
        e = e->NextInAEL;
      }
    } else
    {
      //nonZero, Positive or Negative filling ...
      while (e != &edge)
      {
        edge.WindCnt2 += e->WindDelta;
        e = e->NextInAEL;
      }
    }
  }
//------------------------------------------------------------------------------

  bool Clipper::IsEvenOddFillType(const TEdge &edge) const
  {
    if (edge.PolyTyp == ptSubject)
      return m_SubjFillType == pftEvenOdd;
    else
      return m_ClipFillType == pftEvenOdd;
  }
//------------------------------------------------------------------------------

  bool Clipper::IsEvenOddAltFillType(const TEdge &edge) const
  {
    if (edge.PolyTyp == ptSubject)
      return m_ClipFillType == pftEvenOdd;
    else
      return m_SubjFillType == pftEvenOdd;
  }
//------------------------------------------------------------------------------

  bool Clipper::IsContributing(const TEdge &edge) const
  {
    PolyFillType pft, pft2;
    if (edge.PolyTyp == ptSubject)
    {
      pft = m_SubjFillType;
      pft2 = m_ClipFillType;
    } else
    {
      pft = m_ClipFillType;
      pft2 = m_SubjFillType;
    }

    switch (pft)
    {
      case pftEvenOdd:
        //return false if a subj line has been flagged as inside a subj polygon
        if (edge.WindDelta == 0 && edge.WindCnt != 1)
          return false;
        break;
      case pftNonZero:
        if (Abs(edge.WindCnt) != 1)
          return false;
        break;
      case pftPositive:
        if (edge.WindCnt != 1)
          return false;
        break;
      default: //pftNegative
        if (edge.WindCnt != -1)
          return false;
    }

    switch (m_ClipType)
    {
      case ctIntersection:
        switch (pft2)
        {
          case pftEvenOdd:
          case pftNonZero:
            return (edge.WindCnt2 != 0);
          case pftPositive:
            return (edge.WindCnt2 > 0);
          default:
            return (edge.WindCnt2 < 0);
        }
        break;
      case ctUnion:
        switch (pft2)
        {
          case pftEvenOdd:
          case pftNonZero:
            return (edge.WindCnt2 == 0);
          case pftPositive:
            return (edge.WindCnt2 <= 0);
          default:
            return (edge.WindCnt2 >= 0);
        }
        break;
      case ctDifference:
        if (edge.PolyTyp == ptSubject)
          switch (pft2)
          {
            case pftEvenOdd:
            case pftNonZero:
              return (edge.WindCnt2 == 0);
            case pftPositive:
              return (edge.WindCnt2 <= 0);
            default:
              return (edge.WindCnt2 >= 0);
          }
        else
          switch (pft2)
          {
            case pftEvenOdd:
            case pftNonZero:
              return (edge.WindCnt2 != 0);
            case pftPositive:
              return (edge.WindCnt2 > 0);
            default:
              return (edge.WindCnt2 < 0);
          }
        break;
      case ctXor:
        if (edge.WindDelta == 0) //XOr always contributing unless open
          switch (pft2)
          {
            case pftEvenOdd:
            case pftNonZero:
              return (edge.WindCnt2 == 0);
            case pftPositive:
              return (edge.WindCnt2 <= 0);
            default:
              return (edge.WindCnt2 >= 0);
          }
        else
          return true;
        break;
      default:
        return true;
    }
  }
//------------------------------------------------------------------------------

  OutPt *Clipper::AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &Pt)
  {
    OutPt *result;
    TEdge *e, *prevE;
    if (IsHorizontal(*e2) || (e1->Dx > e2->Dx))
    {
      result = AddOutPt(e1, Pt);
      e2->OutIdx = e1->OutIdx;
      e1->Side = esLeft;
      e2->Side = esRight;
      e = e1;
      if (e->PrevInAEL == e2)
        prevE = e2->PrevInAEL;
      else
        prevE = e->PrevInAEL;
    } else
    {
      result = AddOutPt(e2, Pt);
      e1->OutIdx = e2->OutIdx;
      e1->Side = esRight;
      e2->Side = esLeft;
      e = e2;
      if (e->PrevInAEL == e1)
        prevE = e1->PrevInAEL;
      else
        prevE = e->PrevInAEL;
    }

    if (prevE && prevE->OutIdx >= 0 && prevE->Top.Y < Pt.Y && e->Top.Y < Pt.Y)
    {
      cInt xPrev = TopX(*prevE, Pt.Y);
      cInt xE = TopX(*e, Pt.Y);
      if (xPrev == xE && (e->WindDelta != 0) && (prevE->WindDelta != 0) &&
          SlopesEqual(IntPoint(xPrev, Pt.Y), prevE->Top, IntPoint(xE, Pt.Y), e->Top, m_UseFullRange))
      {
        OutPt *outPt = AddOutPt(prevE, Pt);
        AddJoin(result, outPt, e->Top);
      }
    }
    return result;
  }
//------------------------------------------------------------------------------

  void Clipper::AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &Pt)
  {
    AddOutPt(e1, Pt);
    if (e2->WindDelta == 0)
      AddOutPt(e2, Pt);
    if (e1->OutIdx == e2->OutIdx)
    {
      e1->OutIdx = Unassigned;
      e2->OutIdx = Unassigned;
    } else if (e1->OutIdx < e2->OutIdx)
      AppendPolygon(e1, e2);
    else
      AppendPolygon(e2, e1);
  }
//------------------------------------------------------------------------------

  void Clipper::AddEdgeToSEL(TEdge *edge)
  {
    //SEL pointers in PEdge are reused to build a list of horizontal edges.
    //However, we don't need to worry about order with horizontal edge processing.
    if (!m_SortedEdges)
    {
      m_SortedEdges = edge;
      edge->PrevInSEL = 0;
      edge->NextInSEL = 0;
    } else
    {
      edge->NextInSEL = m_SortedEdges;
      edge->PrevInSEL = 0;
      m_SortedEdges->PrevInSEL = edge;
      m_SortedEdges = edge;
    }
  }
//------------------------------------------------------------------------------

  bool Clipper::PopEdgeFromSEL(TEdge *&edge)
  {
    if (!m_SortedEdges)
      return false;
    edge = m_SortedEdges;
    DeleteFromSEL(m_SortedEdges);
    return true;
  }
//------------------------------------------------------------------------------

  void Clipper::CopyAELToSEL()
  {
    TEdge *e = m_ActiveEdges;
    m_SortedEdges = e;
    while (e)
    {
      e->PrevInSEL = e->PrevInAEL;
      e->NextInSEL = e->NextInAEL;
      e = e->NextInAEL;
    }
  }
//------------------------------------------------------------------------------

  void Clipper::AddJoin(OutPt *op1, OutPt *op2, const IntPoint OffPt)
  {
    Join *j = new Join;
    j->OutPt1 = op1;
    j->OutPt2 = op2;
    j->OffPt = OffPt;
    m_Joins.push_back(j);
  }
//------------------------------------------------------------------------------

  void Clipper::ClearJoins()
  {
    for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
      delete m_Joins[i];
    m_Joins.resize(0);
  }
//------------------------------------------------------------------------------

  void Clipper::ClearGhostJoins()
  {
    for (JoinList::size_type i = 0; i < m_GhostJoins.size(); i++)
      delete m_GhostJoins[i];
    m_GhostJoins.resize(0);
  }
//------------------------------------------------------------------------------

  void Clipper::AddGhostJoin(OutPt *op, const IntPoint OffPt)
  {
    Join *j = new Join;
    j->OutPt1 = op;
    j->OutPt2 = 0;
    j->OffPt = OffPt;
    m_GhostJoins.push_back(j);
  }
//------------------------------------------------------------------------------

  void Clipper::InsertLocalMinimaIntoAEL(const cInt botY)
  {
    const LocalMinimum *lm;
    while (PopLocalMinima(botY, lm))
    {
      TEdge *lb = lm->LeftBound;
      TEdge *rb = lm->RightBound;

      OutPt *Op1 = 0;
      if (!lb)
      {
        //nb: don't insert LB into either AEL or SEL
        InsertEdgeIntoAEL(rb, 0);
        SetWindingCount(*rb);
        if (IsContributing(*rb))
          Op1 = AddOutPt(rb, rb->Bot);
      } else if (!rb)
      {
        InsertEdgeIntoAEL(lb, 0);
        SetWindingCount(*lb);
        if (IsContributing(*lb))
          Op1 = AddOutPt(lb, lb->Bot);
        InsertScanbeam(lb->Top.Y);
      } else
      {
        InsertEdgeIntoAEL(lb, 0);
        InsertEdgeIntoAEL(rb, lb);
        SetWindingCount(*lb);
        rb->WindCnt = lb->WindCnt;
        rb->WindCnt2 = lb->WindCnt2;
        if (IsContributing(*lb))
          Op1 = AddLocalMinPoly(lb, rb, lb->Bot);
        InsertScanbeam(lb->Top.Y);
      }

      if (rb)
      {
        if (IsHorizontal(*rb))
        {
          AddEdgeToSEL(rb);
          if (rb->NextInLML)
            InsertScanbeam(rb->NextInLML->Top.Y);
        } else
          InsertScanbeam(rb->Top.Y);
      }

      if (!lb || !rb)
        continue;

      //if any output polygons share an edge, they'll need joining later ...
      if (Op1 && IsHorizontal(*rb) &&
          m_GhostJoins.size() > 0 && (rb->WindDelta != 0))
      {
        for (JoinList::size_type i = 0; i < m_GhostJoins.size(); ++i)
        {
          Join *jr = m_GhostJoins[i];
          //if the horizontal Rb and a 'ghost' horizontal overlap, then convert
          //the 'ghost' join to a real join ready for later ...
          if (HorzSegmentsOverlap(jr->OutPt1->Pt.X, jr->OffPt.X, rb->Bot.X, rb->Top.X))
            AddJoin(jr->OutPt1, Op1, jr->OffPt);
        }
      }

      if (lb->OutIdx >= 0 && lb->PrevInAEL &&
          lb->PrevInAEL->Curr.X == lb->Bot.X &&
          lb->PrevInAEL->OutIdx >= 0 &&
          SlopesEqual(lb->PrevInAEL->Bot, lb->PrevInAEL->Top, lb->Curr, lb->Top, m_UseFullRange) &&
          (lb->WindDelta != 0) && (lb->PrevInAEL->WindDelta != 0))
      {
        OutPt *Op2 = AddOutPt(lb->PrevInAEL, lb->Bot);
        AddJoin(Op1, Op2, lb->Top);
      }

      if (lb->NextInAEL != rb)
      {

        if (rb->OutIdx >= 0 && rb->PrevInAEL->OutIdx >= 0 &&
            SlopesEqual(rb->PrevInAEL->Curr, rb->PrevInAEL->Top, rb->Curr, rb->Top, m_UseFullRange) &&
            (rb->WindDelta != 0) && (rb->PrevInAEL->WindDelta != 0))
        {
          OutPt *Op2 = AddOutPt(rb->PrevInAEL, rb->Bot);
          AddJoin(Op1, Op2, rb->Top);
        }

        TEdge *e = lb->NextInAEL;
        if (e)
        {
          while (e != rb)
          {
            //nb: For calculating winding counts etc, IntersectEdges() assumes
            //that param1 will be to the Right of param2 ABOVE the intersection ...
            IntersectEdges(rb, e, lb->Curr); //order important here
            e = e->NextInAEL;
          }
        }
      }

    }
  }
//------------------------------------------------------------------------------

  void Clipper::DeleteFromSEL(TEdge *e)
  {
    TEdge *SelPrev = e->PrevInSEL;
    TEdge *SelNext = e->NextInSEL;
    if (!SelPrev && !SelNext && (e != m_SortedEdges))
      return; //already deleted
    if (SelPrev)
      SelPrev->NextInSEL = SelNext;
    else
      m_SortedEdges = SelNext;
    if (SelNext)
      SelNext->PrevInSEL = SelPrev;
    e->NextInSEL = 0;
    e->PrevInSEL = 0;
  }
//------------------------------------------------------------------------------

#ifdef use_xyz
                                                                                                                          void Clipper::SetZ(IntPoint& pt, TEdge& e1, TEdge& e2)
{
  if (pt.Z != 0 || !m_ZFill) return;
  else if (pt == e1.Bot) pt.Z = e1.Bot.Z;
  else if (pt == e1.Top) pt.Z = e1.Top.Z;
  else if (pt == e2.Bot) pt.Z = e2.Bot.Z;
  else if (pt == e2.Top) pt.Z = e2.Top.Z;
  else (*m_ZFill)(e1.Bot, e1.Top, e2.Bot, e2.Top, pt);
}
//------------------------------------------------------------------------------
#endif

  void Clipper::IntersectEdges(TEdge *e1, TEdge *e2, IntPoint &Pt)
  {
    bool e1Contributing = (e1->OutIdx >= 0);
    bool e2Contributing = (e2->OutIdx >= 0);

#ifdef use_xyz
    SetZ(Pt, *e1, *e2);
#endif

#ifdef use_lines
    //if either edge is on an OPEN path ...
    if (e1->WindDelta == 0 || e2->WindDelta == 0)
    {
      //ignore subject-subject open path intersections UNLESS they
      //are both open paths, AND they are both 'contributing maximas' ...
      if (e1->WindDelta == 0 && e2->WindDelta == 0)
        return;

        //if intersecting a subj line with a subj poly ...
      else if (e1->PolyTyp == e2->PolyTyp &&
               e1->WindDelta != e2->WindDelta && m_ClipType == ctUnion)
      {
        if (e1->WindDelta == 0)
        {
          if (e2Contributing)
          {
            AddOutPt(e1, Pt);
            if (e1Contributing)
              e1->OutIdx = Unassigned;
          }
        } else
        {
          if (e1Contributing)
          {
            AddOutPt(e2, Pt);
            if (e2Contributing)
              e2->OutIdx = Unassigned;
          }
        }
      } else if (e1->PolyTyp != e2->PolyTyp)
      {
        //toggle subj open path OutIdx on/off when Abs(clip.WndCnt) == 1 ...
        if ((e1->WindDelta == 0) && abs(e2->WindCnt) == 1 &&
            (m_ClipType != ctUnion || e2->WindCnt2 == 0))
        {
          AddOutPt(e1, Pt);
          if (e1Contributing)
            e1->OutIdx = Unassigned;
        } else if ((e2->WindDelta == 0) && (abs(e1->WindCnt) == 1) &&
                   (m_ClipType != ctUnion || e1->WindCnt2 == 0))
        {
          AddOutPt(e2, Pt);
          if (e2Contributing)
            e2->OutIdx = Unassigned;
        }
      }
      return;
    }
#endif

    //update winding counts...
    //assumes that e1 will be to the Right of e2 ABOVE the intersection
    if (e1->PolyTyp == e2->PolyTyp)
    {
      if (IsEvenOddFillType(*e1))
      {
        int oldE1WindCnt = e1->WindCnt;
        e1->WindCnt = e2->WindCnt;
        e2->WindCnt = oldE1WindCnt;
      } else
      {
        if (e1->WindCnt + e2->WindDelta == 0)
          e1->WindCnt = -e1->WindCnt;
        else
          e1->WindCnt += e2->WindDelta;
        if (e2->WindCnt - e1->WindDelta == 0)
          e2->WindCnt = -e2->WindCnt;
        else
          e2->WindCnt -= e1->WindDelta;
      }
    } else
    {
      if (!IsEvenOddFillType(*e2))
        e1->WindCnt2 += e2->WindDelta;
      else
        e1->WindCnt2 = (e1->WindCnt2 == 0) ? 1 : 0;
      if (!IsEvenOddFillType(*e1))
        e2->WindCnt2 -= e1->WindDelta;
      else
        e2->WindCnt2 = (e2->WindCnt2 == 0) ? 1 : 0;
    }

    PolyFillType e1FillType, e2FillType, e1FillType2, e2FillType2;
    if (e1->PolyTyp == ptSubject)
    {
      e1FillType = m_SubjFillType;
      e1FillType2 = m_ClipFillType;
    } else
    {
      e1FillType = m_ClipFillType;
      e1FillType2 = m_SubjFillType;
    }
    if (e2->PolyTyp == ptSubject)
    {
      e2FillType = m_SubjFillType;
      e2FillType2 = m_ClipFillType;
    } else
    {
      e2FillType = m_ClipFillType;
      e2FillType2 = m_SubjFillType;
    }

    cInt e1Wc, e2Wc;
    switch (e1FillType)
    {
      case pftPositive:
        e1Wc = e1->WindCnt;
        break;
      case pftNegative:
        e1Wc = -e1->WindCnt;
        break;
      default:
        e1Wc = Abs(e1->WindCnt);
    }
    switch (e2FillType)
    {
      case pftPositive:
        e2Wc = e2->WindCnt;
        break;
      case pftNegative:
        e2Wc = -e2->WindCnt;
        break;
      default:
        e2Wc = Abs(e2->WindCnt);
    }

    if (e1Contributing && e2Contributing)
    {
      if ((e1Wc != 0 && e1Wc != 1) || (e2Wc != 0 && e2Wc != 1) ||
          (e1->PolyTyp != e2->PolyTyp && m_ClipType != ctXor))
      {
        AddLocalMaxPoly(e1, e2, Pt);
      } else
      {
        AddOutPt(e1, Pt);
        AddOutPt(e2, Pt);
        SwapSides(*e1, *e2);
        SwapPolyIndexes(*e1, *e2);
      }
    } else if (e1Contributing)
    {
      if (e2Wc == 0 || e2Wc == 1)
      {
        AddOutPt(e1, Pt);
        SwapSides(*e1, *e2);
        SwapPolyIndexes(*e1, *e2);
      }
    } else if (e2Contributing)
    {
      if (e1Wc == 0 || e1Wc == 1)
      {
        AddOutPt(e2, Pt);
        SwapSides(*e1, *e2);
        SwapPolyIndexes(*e1, *e2);
      }
    } else if ((e1Wc == 0 || e1Wc == 1) && (e2Wc == 0 || e2Wc == 1))
    {
      //neither edge is currently contributing ...

      cInt e1Wc2, e2Wc2;
      switch (e1FillType2)
      {
        case pftPositive:
          e1Wc2 = e1->WindCnt2;
          break;
        case pftNegative :
          e1Wc2 = -e1->WindCnt2;
          break;
        default:
          e1Wc2 = Abs(e1->WindCnt2);
      }
      switch (e2FillType2)
      {
        case pftPositive:
          e2Wc2 = e2->WindCnt2;
          break;
        case pftNegative:
          e2Wc2 = -e2->WindCnt2;
          break;
        default:
          e2Wc2 = Abs(e2->WindCnt2);
      }

      if (e1->PolyTyp != e2->PolyTyp)
      {
        AddLocalMinPoly(e1, e2, Pt);
      } else if (e1Wc == 1 && e2Wc == 1)
        switch (m_ClipType)
        {
          case ctIntersection:
            if (e1Wc2 > 0 && e2Wc2 > 0)
              AddLocalMinPoly(e1, e2, Pt);
            break;
          case ctUnion:
            if (e1Wc2 <= 0 && e2Wc2 <= 0)
              AddLocalMinPoly(e1, e2, Pt);
            break;
          case ctDifference:
            if (((e1->PolyTyp == ptClip) && (e1Wc2 > 0) && (e2Wc2 > 0)) ||
                ((e1->PolyTyp == ptSubject) && (e1Wc2 <= 0) && (e2Wc2 <= 0)))
              AddLocalMinPoly(e1, e2, Pt);
            break;
          case ctXor:
            AddLocalMinPoly(e1, e2, Pt);
        }
      else
        SwapSides(*e1, *e2);
    }
  }
//------------------------------------------------------------------------------

  void Clipper::SetHoleState(TEdge *e, OutRec *outrec)
  {
    TEdge *e2 = e->PrevInAEL;
    TEdge *eTmp = 0;
    while (e2)
    {
      if (e2->OutIdx >= 0 && e2->WindDelta != 0)
      {
        if (!eTmp)
          eTmp = e2;
        else if (eTmp->OutIdx == e2->OutIdx)
          eTmp = 0;
      }
      e2 = e2->PrevInAEL;
    }
    if (!eTmp)
    {
      outrec->FirstLeft = 0;
      outrec->IsHole = false;
    } else
    {
      outrec->FirstLeft = m_PolyOuts[eTmp->OutIdx];
      outrec->IsHole = !outrec->FirstLeft->IsHole;
    }
  }
//------------------------------------------------------------------------------

  OutRec *GetLowermostRec(OutRec *outRec1, OutRec *outRec2)
  {
    //work out which polygon fragment has the correct hole state ...
    if (!outRec1->BottomPt)
      outRec1->BottomPt = GetBottomPt(outRec1->Pts);
    if (!outRec2->BottomPt)
      outRec2->BottomPt = GetBottomPt(outRec2->Pts);
    OutPt *OutPt1 = outRec1->BottomPt;
    OutPt *OutPt2 = outRec2->BottomPt;
    if (OutPt1->Pt.Y > OutPt2->Pt.Y)
      return outRec1;
    else if (OutPt1->Pt.Y < OutPt2->Pt.Y)
      return outRec2;
    else if (OutPt1->Pt.X < OutPt2->Pt.X)
      return outRec1;
    else if (OutPt1->Pt.X > OutPt2->Pt.X)
      return outRec2;
    else if (OutPt1->Next == OutPt1)
      return outRec2;
    else if (OutPt2->Next == OutPt2)
      return outRec1;
    else if (FirstIsBottomPt(OutPt1, OutPt2))
      return outRec1;
    else
      return outRec2;
  }
//------------------------------------------------------------------------------

  bool OutRec1RightOfOutRec2(OutRec *outRec1, OutRec *outRec2)
  {
    do
    {
      outRec1 = outRec1->FirstLeft;
      if (outRec1 == outRec2)
        return true;
    } while (outRec1);
    return false;
  }
//------------------------------------------------------------------------------

  OutRec *Clipper::GetOutRec(int Idx)
  {
    OutRec *outrec = m_PolyOuts[Idx];
    while (outrec != m_PolyOuts[outrec->Idx])
      outrec = m_PolyOuts[outrec->Idx];
    return outrec;
  }
//------------------------------------------------------------------------------

  void Clipper::AppendPolygon(TEdge *e1, TEdge *e2)
  {
    //get the start and ends of both output polygons ...
    OutRec *outRec1 = m_PolyOuts[e1->OutIdx];
    OutRec *outRec2 = m_PolyOuts[e2->OutIdx];

    OutRec *holeStateRec;
    if (OutRec1RightOfOutRec2(outRec1, outRec2))
      holeStateRec = outRec2;
    else if (OutRec1RightOfOutRec2(outRec2, outRec1))
      holeStateRec = outRec1;
    else
      holeStateRec = GetLowermostRec(outRec1, outRec2);

    //get the start and ends of both output polygons and
    //join e2 poly onto e1 poly and delete pointers to e2 ...

    OutPt *p1_lft = outRec1->Pts;
    OutPt *p1_rt = p1_lft->Prev;
    OutPt *p2_lft = outRec2->Pts;
    OutPt *p2_rt = p2_lft->Prev;

    //join e2 poly onto e1 poly and delete pointers to e2 ...
    if (e1->Side == esLeft)
    {
      if (e2->Side == esLeft)
      {
        //z y x a b c
        ReversePolyPtLinks(p2_lft);
        p2_lft->Next = p1_lft;
        p1_lft->Prev = p2_lft;
        p1_rt->Next = p2_rt;
        p2_rt->Prev = p1_rt;
        outRec1->Pts = p2_rt;
      } else
      {
        //x y z a b c
        p2_rt->Next = p1_lft;
        p1_lft->Prev = p2_rt;
        p2_lft->Prev = p1_rt;
        p1_rt->Next = p2_lft;
        outRec1->Pts = p2_lft;
      }
    } else
    {
      if (e2->Side == esRight)
      {
        //a b c z y x
        ReversePolyPtLinks(p2_lft);
        p1_rt->Next = p2_rt;
        p2_rt->Prev = p1_rt;
        p2_lft->Next = p1_lft;
        p1_lft->Prev = p2_lft;
      } else
      {
        //a b c x y z
        p1_rt->Next = p2_lft;
        p2_lft->Prev = p1_rt;
        p1_lft->Prev = p2_rt;
        p2_rt->Next = p1_lft;
      }
    }

    outRec1->BottomPt = 0;
    if (holeStateRec == outRec2)
    {
      if (outRec2->FirstLeft != outRec1)
        outRec1->FirstLeft = outRec2->FirstLeft;
      outRec1->IsHole = outRec2->IsHole;
    }
    outRec2->Pts = 0;
    outRec2->BottomPt = 0;
    outRec2->FirstLeft = outRec1;

    int OKIdx = e1->OutIdx;
    int ObsoleteIdx = e2->OutIdx;

    e1->OutIdx = Unassigned; //nb: safe because we only get here via AddLocalMaxPoly
    e2->OutIdx = Unassigned;

    TEdge *e = m_ActiveEdges;
    while (e)
    {
      if (e->OutIdx == ObsoleteIdx)
      {
        e->OutIdx = OKIdx;
        e->Side = e1->Side;
        break;
      }
      e = e->NextInAEL;
    }

    outRec2->Idx = outRec1->Idx;
  }
//------------------------------------------------------------------------------

  OutPt *Clipper::AddOutPt(TEdge *e, const IntPoint &pt)
  {
    if (e->OutIdx < 0)
    {
      OutRec *outRec = CreateOutRec();
      outRec->IsOpen = (e->WindDelta == 0);
      OutPt *newOp = new OutPt;
      outRec->Pts = newOp;
      newOp->Idx = outRec->Idx;
      newOp->Pt = pt;
      newOp->Next = newOp;
      newOp->Prev = newOp;
      if (!outRec->IsOpen)
        SetHoleState(e, outRec);
      e->OutIdx = outRec->Idx;
      return newOp;
    } else
    {
      OutRec *outRec = m_PolyOuts[e->OutIdx];
      //OutRec.Pts is the 'Left-most' point & OutRec.Pts.Prev is the 'Right-most'
      OutPt *op = outRec->Pts;

      bool ToFront = (e->Side == esLeft);
      if (ToFront && (pt == op->Pt))
        return op;
      else if (!ToFront && (pt == op->Prev->Pt))
        return op->Prev;

      OutPt *newOp = new OutPt;
      newOp->Idx = outRec->Idx;
      newOp->Pt = pt;
      newOp->Next = op;
      newOp->Prev = op->Prev;
      newOp->Prev->Next = newOp;
      op->Prev = newOp;
      if (ToFront)
        outRec->Pts = newOp;
      return newOp;
    }
  }
//------------------------------------------------------------------------------

  OutPt *Clipper::GetLastOutPt(TEdge *e)
  {
    OutRec *outRec = m_PolyOuts[e->OutIdx];
    if (e->Side == esLeft)
      return outRec->Pts;
    else
      return outRec->Pts->Prev;
  }
//------------------------------------------------------------------------------

  void Clipper::ProcessHorizontals()
  {
    TEdge *horzEdge;
    while (PopEdgeFromSEL(horzEdge))
      ProcessHorizontal(horzEdge);
  }
//------------------------------------------------------------------------------

  inline bool IsMinima(TEdge *e)
  {
    return e && (e->Prev->NextInLML != e) && (e->Next->NextInLML != e);
  }
//------------------------------------------------------------------------------

  inline bool IsMaxima(TEdge *e, const cInt Y)
  {
    return e && e->Top.Y == Y && !e->NextInLML;
  }
//------------------------------------------------------------------------------

  inline bool IsIntermediate(TEdge *e, const cInt Y)
  {
    return e->Top.Y == Y && e->NextInLML;
  }
//------------------------------------------------------------------------------

  TEdge *GetMaximaPair(TEdge *e)
  {
    if ((e->Next->Top == e->Top) && !e->Next->NextInLML)
      return e->Next;
    else if ((e->Prev->Top == e->Top) && !e->Prev->NextInLML)
      return e->Prev;
    else
      return 0;
  }
//------------------------------------------------------------------------------

  TEdge *GetMaximaPairEx(TEdge *e)
  {
    //as GetMaximaPair() but returns 0 if MaxPair isn't in AEL (unless it's horizontal)
    TEdge *result = GetMaximaPair(e);
    if (result && (result->OutIdx == Skip ||
                   (result->NextInAEL == result->PrevInAEL && !IsHorizontal(*result))))
      return 0;
    return result;
  }
//------------------------------------------------------------------------------

  void Clipper::SwapPositionsInSEL(TEdge *Edge1, TEdge *Edge2)
  {
    if (!(Edge1->NextInSEL) && !(Edge1->PrevInSEL))
      return;
    if (!(Edge2->NextInSEL) && !(Edge2->PrevInSEL))
      return;

    if (Edge1->NextInSEL == Edge2)
    {
      TEdge *Next = Edge2->NextInSEL;
      if (Next)
        Next->PrevInSEL = Edge1;
      TEdge *Prev = Edge1->PrevInSEL;
      if (Prev)
        Prev->NextInSEL = Edge2;
      Edge2->PrevInSEL = Prev;
      Edge2->NextInSEL = Edge1;
      Edge1->PrevInSEL = Edge2;
      Edge1->NextInSEL = Next;
    } else if (Edge2->NextInSEL == Edge1)
    {
      TEdge *Next = Edge1->NextInSEL;
      if (Next)
        Next->PrevInSEL = Edge2;
      TEdge *Prev = Edge2->PrevInSEL;
      if (Prev)
        Prev->NextInSEL = Edge1;
      Edge1->PrevInSEL = Prev;
      Edge1->NextInSEL = Edge2;
      Edge2->PrevInSEL = Edge1;
      Edge2->NextInSEL = Next;
    } else
    {
      TEdge *Next = Edge1->NextInSEL;
      TEdge *Prev = Edge1->PrevInSEL;
      Edge1->NextInSEL = Edge2->NextInSEL;
      if (Edge1->NextInSEL)
        Edge1->NextInSEL->PrevInSEL = Edge1;
      Edge1->PrevInSEL = Edge2->PrevInSEL;
      if (Edge1->PrevInSEL)
        Edge1->PrevInSEL->NextInSEL = Edge1;
      Edge2->NextInSEL = Next;
      if (Edge2->NextInSEL)
        Edge2->NextInSEL->PrevInSEL = Edge2;
      Edge2->PrevInSEL = Prev;
      if (Edge2->PrevInSEL)
        Edge2->PrevInSEL->NextInSEL = Edge2;
    }

    if (!Edge1->PrevInSEL)
      m_SortedEdges = Edge1;
    else if (!Edge2->PrevInSEL)
      m_SortedEdges = Edge2;
  }
//------------------------------------------------------------------------------

  TEdge *GetNextInAEL(TEdge *e, Direction dir)
  {
    return dir == dLeftToRight ? e->NextInAEL : e->PrevInAEL;
  }
//------------------------------------------------------------------------------

  void GetHorzDirection(TEdge &HorzEdge, Direction &Dir, cInt &Left, cInt &Right)
  {
    if (HorzEdge.Bot.X < HorzEdge.Top.X)
    {
      Left = HorzEdge.Bot.X;
      Right = HorzEdge.Top.X;
      Dir = dLeftToRight;
    } else
    {
      Left = HorzEdge.Top.X;
      Right = HorzEdge.Bot.X;
      Dir = dRightToLeft;
    }
  }
//------------------------------------------------------------------------

/*******************************************************************************
* Notes: Horizontal edges (HEs) at scanline intersections (ie at the Top or    *
* Bottom of a scanbeam) are processed as if layered. The order in which HEs    *
* are processed doesn't matter. HEs intersect with other HE Bot.Xs only [#]    *
* (or they could intersect with Top.Xs only, ie EITHER Bot.Xs OR Top.Xs),      *
* and with other non-horizontal edges [*]. Once these intersections are        *
* processed, intermediate HEs then 'promote' the Edge above (NextInLML) into   *
* the AEL. These 'promoted' edges may in turn intersect [%] with other HEs.    *
*******************************************************************************/

  void Clipper::ProcessHorizontal(TEdge *horzEdge)
  {
    Direction dir;
    cInt horzLeft, horzRight;
    bool IsOpen = (horzEdge->WindDelta == 0);

    GetHorzDirection(*horzEdge, dir, horzLeft, horzRight);

    TEdge *eLastHorz = horzEdge, *eMaxPair = 0;
    while (eLastHorz->NextInLML && IsHorizontal(*eLastHorz->NextInLML))
      eLastHorz = eLastHorz->NextInLML;
    if (!eLastHorz->NextInLML)
      eMaxPair = GetMaximaPair(eLastHorz);

    MaximaList::const_iterator maxIt;
    MaximaList::const_reverse_iterator maxRit;
    if (m_Maxima.size() > 0)
    {
      //get the first maxima in range (X) ...
      if (dir == dLeftToRight)
      {
        maxIt = m_Maxima.begin();
        while (maxIt != m_Maxima.end() && *maxIt <= horzEdge->Bot.X)
          maxIt++;
        if (maxIt != m_Maxima.end() && *maxIt >= eLastHorz->Top.X)
          maxIt = m_Maxima.end();
      } else
      {
        maxRit = m_Maxima.rbegin();
        while (maxRit != m_Maxima.rend() && *maxRit > horzEdge->Bot.X)
          maxRit++;
        if (maxRit != m_Maxima.rend() && *maxRit <= eLastHorz->Top.X)
          maxRit = m_Maxima.rend();
      }
    }

    OutPt *op1 = 0;

    for (;;) //loop through consec. horizontal edges
    {

      bool IsLastHorz = (horzEdge == eLastHorz);
      TEdge *e = GetNextInAEL(horzEdge, dir);
      while (e)
      {

        //this code block inserts extra coords into horizontal edges (in output
        //polygons) whereever maxima touch these horizontal edges. This helps
        //'simplifying' polygons (ie if the Simplify property is set).
        if (m_Maxima.size() > 0)
        {
          if (dir == dLeftToRight)
          {
            while (maxIt != m_Maxima.end() && *maxIt < e->Curr.X)
            {
              if (horzEdge->OutIdx >= 0 && !IsOpen)
                AddOutPt(horzEdge, IntPoint(*maxIt, horzEdge->Bot.Y));
              maxIt++;
            }
          } else
          {
            while (maxRit != m_Maxima.rend() && *maxRit > e->Curr.X)
            {
              if (horzEdge->OutIdx >= 0 && !IsOpen)
                AddOutPt(horzEdge, IntPoint(*maxRit, horzEdge->Bot.Y));
              maxRit++;
            }
          }
        };

        if ((dir == dLeftToRight && e->Curr.X > horzRight) ||
            (dir == dRightToLeft && e->Curr.X < horzLeft))
          break;

        //Also break if we've got to the end of an intermediate horizontal edge ...
        //nb: Smaller Dx's are to the right of larger Dx's ABOVE the horizontal.
        if (e->Curr.X == horzEdge->Top.X && horzEdge->NextInLML &&
            e->Dx < horzEdge->NextInLML->Dx)
          break;

        if (horzEdge->OutIdx >= 0 && !IsOpen)  //note: may be done multiple times
        {
#ifdef use_xyz
                                                                                                                                  if (dir == dLeftToRight) SetZ(e->Curr, *horzEdge, *e);
      else SetZ(e->Curr, *e, *horzEdge);
#endif
          op1 = AddOutPt(horzEdge, e->Curr);
          TEdge *eNextHorz = m_SortedEdges;
          while (eNextHorz)
          {
            if (eNextHorz->OutIdx >= 0 &&
                HorzSegmentsOverlap(horzEdge->Bot.X,
                                    horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X))
            {
              OutPt *op2 = GetLastOutPt(eNextHorz);
              AddJoin(op2, op1, eNextHorz->Top);
            }
            eNextHorz = eNextHorz->NextInSEL;
          }
          AddGhostJoin(op1, horzEdge->Bot);
        }

        //OK, so far we're still in range of the horizontal Edge  but make sure
        //we're at the last of consec. horizontals when matching with eMaxPair
        if (e == eMaxPair && IsLastHorz)
        {
          if (horzEdge->OutIdx >= 0)
            AddLocalMaxPoly(horzEdge, eMaxPair, horzEdge->Top);
          DeleteFromAEL(horzEdge);
          DeleteFromAEL(eMaxPair);
          return;
        }

        if (dir == dLeftToRight)
        {
          IntPoint Pt = IntPoint(e->Curr.X, horzEdge->Curr.Y);
          IntersectEdges(horzEdge, e, Pt);
        } else
        {
          IntPoint Pt = IntPoint(e->Curr.X, horzEdge->Curr.Y);
          IntersectEdges(e, horzEdge, Pt);
        }
        TEdge *eNext = GetNextInAEL(e, dir);
        SwapPositionsInAEL(horzEdge, e);
        e = eNext;
      } //end while(e)

      //Break out of loop if HorzEdge.NextInLML is not also horizontal ...
      if (!horzEdge->NextInLML || !IsHorizontal(*horzEdge->NextInLML))
        break;

      UpdateEdgeIntoAEL(horzEdge);
      if (horzEdge->OutIdx >= 0)
        AddOutPt(horzEdge, horzEdge->Bot);
      GetHorzDirection(*horzEdge, dir, horzLeft, horzRight);

    } //end for (;;)

    if (horzEdge->OutIdx >= 0 && !op1)
    {
      op1 = GetLastOutPt(horzEdge);
      TEdge *eNextHorz = m_SortedEdges;
      while (eNextHorz)
      {
        if (eNextHorz->OutIdx >= 0 &&
            HorzSegmentsOverlap(horzEdge->Bot.X,
                                horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X))
        {
          OutPt *op2 = GetLastOutPt(eNextHorz);
          AddJoin(op2, op1, eNextHorz->Top);
        }
        eNextHorz = eNextHorz->NextInSEL;
      }
      AddGhostJoin(op1, horzEdge->Top);
    }

    if (horzEdge->NextInLML)
    {
      if (horzEdge->OutIdx >= 0)
      {
        op1 = AddOutPt(horzEdge, horzEdge->Top);
        UpdateEdgeIntoAEL(horzEdge);
        if (horzEdge->WindDelta == 0)
          return;
        //nb: HorzEdge is no longer horizontal here
        TEdge *ePrev = horzEdge->PrevInAEL;
        TEdge *eNext = horzEdge->NextInAEL;
        if (ePrev && ePrev->Curr.X == horzEdge->Bot.X &&
            ePrev->Curr.Y == horzEdge->Bot.Y && ePrev->WindDelta != 0 &&
            (ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y &&
             SlopesEqual(*horzEdge, *ePrev, m_UseFullRange)))
        {
          OutPt *op2 = AddOutPt(ePrev, horzEdge->Bot);
          AddJoin(op1, op2, horzEdge->Top);
        } else if (eNext && eNext->Curr.X == horzEdge->Bot.X &&
                   eNext->Curr.Y == horzEdge->Bot.Y && eNext->WindDelta != 0 &&
                   eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y &&
                   SlopesEqual(*horzEdge, *eNext, m_UseFullRange))
        {
          OutPt *op2 = AddOutPt(eNext, horzEdge->Bot);
          AddJoin(op1, op2, horzEdge->Top);
        }
      } else
        UpdateEdgeIntoAEL(horzEdge);
    } else
    {
      if (horzEdge->OutIdx >= 0)
        AddOutPt(horzEdge, horzEdge->Top);
      DeleteFromAEL(horzEdge);
    }
  }
//------------------------------------------------------------------------------

  bool Clipper::ProcessIntersections(const cInt topY)
  {
    if (!m_ActiveEdges)
      return true;
    try
    {
      BuildIntersectList(topY);
      size_t IlSize = m_IntersectList.size();
      if (IlSize == 0)
        return true;
      if (IlSize == 1 || FixupIntersectionOrder())
        ProcessIntersectList();
      else
        return false;
    }
    catch (...)
    {
      m_SortedEdges = 0;
      DisposeIntersectNodes();
      throw clipperException("ProcessIntersections error");
    }
    m_SortedEdges = 0;
    return true;
  }
//------------------------------------------------------------------------------

  void Clipper::DisposeIntersectNodes()
  {
    for (size_t i = 0; i < m_IntersectList.size(); ++i)
      delete m_IntersectList[i];
    m_IntersectList.clear();
  }
//------------------------------------------------------------------------------

  void Clipper::BuildIntersectList(const cInt topY)
  {
    if (!m_ActiveEdges)
      return;

    //prepare for sorting ...
    TEdge *e = m_ActiveEdges;
    m_SortedEdges = e;
    while (e)
    {
      e->PrevInSEL = e->PrevInAEL;
      e->NextInSEL = e->NextInAEL;
      e->Curr.X = TopX(*e, topY);
      e = e->NextInAEL;
    }

    //bubblesort ...
    bool isModified;
    do
    {
      isModified = false;
      e = m_SortedEdges;
      while (e->NextInSEL)
      {
        TEdge *eNext = e->NextInSEL;
        IntPoint Pt;
        if (e->Curr.X > eNext->Curr.X)
        {
          IntersectPoint(*e, *eNext, Pt);
          if (Pt.Y < topY)
            Pt = IntPoint(TopX(*e, topY), topY);
          IntersectNode *newNode = new IntersectNode;
          newNode->Edge1 = e;
          newNode->Edge2 = eNext;
          newNode->Pt = Pt;
          m_IntersectList.push_back(newNode);

          SwapPositionsInSEL(e, eNext);
          isModified = true;
        } else
          e = eNext;
      }
      if (e->PrevInSEL)
        e->PrevInSEL->NextInSEL = 0;
      else
        break;
    } while (isModified);
    m_SortedEdges = 0; //important
  }
//------------------------------------------------------------------------------


  void Clipper::ProcessIntersectList()
  {
    for (size_t i = 0; i < m_IntersectList.size(); ++i)
    {
      IntersectNode *iNode = m_IntersectList[i];
      {
        IntersectEdges(iNode->Edge1, iNode->Edge2, iNode->Pt);
        SwapPositionsInAEL(iNode->Edge1, iNode->Edge2);
      }
      delete iNode;
    }
    m_IntersectList.clear();
  }
//------------------------------------------------------------------------------

  bool IntersectListSort(IntersectNode *node1, IntersectNode *node2)
  {
    return node2->Pt.Y < node1->Pt.Y;
  }
//------------------------------------------------------------------------------

  inline bool EdgesAdjacent(const IntersectNode &inode)
  {
    return (inode.Edge1->NextInSEL == inode.Edge2) ||
           (inode.Edge1->PrevInSEL == inode.Edge2);
  }
//------------------------------------------------------------------------------

  bool Clipper::FixupIntersectionOrder()
  {
    //pre-condition: intersections are sorted Bottom-most first.
    //Now it's crucial that intersections are made only between adjacent edges,
    //so to ensure this the order of intersections may need adjusting ...
    CopyAELToSEL();
    std::sort(m_IntersectList.begin(), m_IntersectList.end(), IntersectListSort);
    size_t cnt = m_IntersectList.size();
    for (size_t i = 0; i < cnt; ++i)
    {
      if (!EdgesAdjacent(*m_IntersectList[i]))
      {
        size_t j = i + 1;
        while (j < cnt && !EdgesAdjacent(*m_IntersectList[j]))
          j++;
        if (j == cnt)
          return false;
        std::swap(m_IntersectList[i], m_IntersectList[j]);
      }
      SwapPositionsInSEL(m_IntersectList[i]->Edge1, m_IntersectList[i]->Edge2);
    }
    return true;
  }
//------------------------------------------------------------------------------

  void Clipper::DoMaxima(TEdge *e)
  {
    TEdge *eMaxPair = GetMaximaPairEx(e);
    if (!eMaxPair)
    {
      if (e->OutIdx >= 0)
        AddOutPt(e, e->Top);
      DeleteFromAEL(e);
      return;
    }

    TEdge *eNext = e->NextInAEL;
    while (eNext && eNext != eMaxPair)
    {
      IntersectEdges(e, eNext, e->Top);
      SwapPositionsInAEL(e, eNext);
      eNext = e->NextInAEL;
    }

    if (e->OutIdx == Unassigned && eMaxPair->OutIdx == Unassigned)
    {
      DeleteFromAEL(e);
      DeleteFromAEL(eMaxPair);
    } else if (e->OutIdx >= 0 && eMaxPair->OutIdx >= 0)
    {
      if (e->OutIdx >= 0)
        AddLocalMaxPoly(e, eMaxPair, e->Top);
      DeleteFromAEL(e);
      DeleteFromAEL(eMaxPair);
    }
#ifdef use_lines
    else if (e->WindDelta == 0)
    {
      if (e->OutIdx >= 0)
      {
        AddOutPt(e, e->Top);
        e->OutIdx = Unassigned;
      }
      DeleteFromAEL(e);

      if (eMaxPair->OutIdx >= 0)
      {
        AddOutPt(eMaxPair, e->Top);
        eMaxPair->OutIdx = Unassigned;
      }
      DeleteFromAEL(eMaxPair);
    }
#endif
    else
      throw clipperException("DoMaxima error");
  }
//------------------------------------------------------------------------------

  void Clipper::ProcessEdgesAtTopOfScanbeam(const cInt topY)
  {
    TEdge *e = m_ActiveEdges;
    while (e)
    {
      //1. process maxima, treating them as if they're 'bent' horizontal edges,
      //   but exclude maxima with horizontal edges. nb: e can't be a horizontal.
      bool IsMaximaEdge = IsMaxima(e, topY);

      if (IsMaximaEdge)
      {
        TEdge *eMaxPair = GetMaximaPairEx(e);
        IsMaximaEdge = (!eMaxPair || !IsHorizontal(*eMaxPair));
      }

      if (IsMaximaEdge)
      {
        if (m_StrictSimple)
          m_Maxima.push_back(e->Top.X);
        TEdge *ePrev = e->PrevInAEL;
        DoMaxima(e);
        if (!ePrev)
          e = m_ActiveEdges;
        else
          e = ePrev->NextInAEL;
      } else
      {
        //2. promote horizontal edges, otherwise update Curr.X and Curr.Y ...
        if (IsIntermediate(e, topY) && IsHorizontal(*e->NextInLML))
        {
          UpdateEdgeIntoAEL(e);
          if (e->OutIdx >= 0)
            AddOutPt(e, e->Bot);
          AddEdgeToSEL(e);
        } else
        {
          e->Curr.X = TopX(*e, topY);
          e->Curr.Y = topY;
#ifdef use_xyz
          e->Curr.Z = topY == e->Top.Y ? e->Top.Z : (topY == e->Bot.Y ? e->Bot.Z : 0);
#endif
        }

        //When StrictlySimple and 'e' is being touched by another edge, then
        //make sure both edges have a vertex here ...
        if (m_StrictSimple)
        {
          TEdge *ePrev = e->PrevInAEL;
          if ((e->OutIdx >= 0) && (e->WindDelta != 0) && ePrev && (ePrev->OutIdx >= 0) &&
              (ePrev->Curr.X == e->Curr.X) && (ePrev->WindDelta != 0))
          {
            IntPoint pt = e->Curr;
#ifdef use_xyz
            SetZ(pt, *ePrev, *e);
#endif
            OutPt *op = AddOutPt(ePrev, pt);
            OutPt *op2 = AddOutPt(e, pt);
            AddJoin(op, op2, pt); //StrictlySimple (type-3) join
          }
        }

        e = e->NextInAEL;
      }
    }

    //3. Process horizontals at the Top of the scanbeam ...
    m_Maxima.sort();
    ProcessHorizontals();
    m_Maxima.clear();

    //4. Promote intermediate vertices ...
    e = m_ActiveEdges;
    while (e)
    {
      if (IsIntermediate(e, topY))
      {
        OutPt *op = 0;
        if (e->OutIdx >= 0)
          op = AddOutPt(e, e->Top);
        UpdateEdgeIntoAEL(e);

        //if output polygons share an edge, they'll need joining later ...
        TEdge *ePrev = e->PrevInAEL;
        TEdge *eNext = e->NextInAEL;
        if (ePrev && ePrev->Curr.X == e->Bot.X &&
            ePrev->Curr.Y == e->Bot.Y && op &&
            ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y &&
            SlopesEqual(e->Curr, e->Top, ePrev->Curr, ePrev->Top, m_UseFullRange) &&
            (e->WindDelta != 0) && (ePrev->WindDelta != 0))
        {
          OutPt *op2 = AddOutPt(ePrev, e->Bot);
          AddJoin(op, op2, e->Top);
        } else if (eNext && eNext->Curr.X == e->Bot.X &&
                   eNext->Curr.Y == e->Bot.Y && op &&
                   eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y &&
                   SlopesEqual(e->Curr, e->Top, eNext->Curr, eNext->Top, m_UseFullRange) &&
                   (e->WindDelta != 0) && (eNext->WindDelta != 0))
        {
          OutPt *op2 = AddOutPt(eNext, e->Bot);
          AddJoin(op, op2, e->Top);
        }
      }
      e = e->NextInAEL;
    }
  }
//------------------------------------------------------------------------------

  void Clipper::FixupOutPolyline(OutRec &outrec)
  {
    OutPt *pp = outrec.Pts;
    OutPt *lastPP = pp->Prev;
    while (pp != lastPP)
    {
      pp = pp->Next;
      if (pp->Pt == pp->Prev->Pt)
      {
        if (pp == lastPP)
          lastPP = pp->Prev;
        OutPt *tmpPP = pp->Prev;
        tmpPP->Next = pp->Next;
        pp->Next->Prev = tmpPP;
        delete pp;
        pp = tmpPP;
      }
    }

    if (pp == pp->Prev)
    {
      DisposeOutPts(pp);
      outrec.Pts = 0;
      return;
    }
  }
//------------------------------------------------------------------------------

  void Clipper::FixupOutPolygon(OutRec &outrec)
  {
    //FixupOutPolygon() - removes duplicate points and simplifies consecutive
    //parallel edges by removing the middle vertex.
    OutPt *lastOK = 0;
    outrec.BottomPt = 0;
    OutPt *pp = outrec.Pts;
    bool preserveCol = m_PreserveCollinear || m_StrictSimple;

    for (;;)
    {
      if (pp->Prev == pp || pp->Prev == pp->Next)
      {
        DisposeOutPts(pp);
        outrec.Pts = 0;
        return;
      }

      //test for duplicate points and collinear edges ...
      if ((pp->Pt == pp->Next->Pt) || (pp->Pt == pp->Prev->Pt) ||
          (SlopesEqual(pp->Prev->Pt, pp->Pt, pp->Next->Pt, m_UseFullRange) &&
           (!preserveCol || !Pt2IsBetweenPt1AndPt3(pp->Prev->Pt, pp->Pt, pp->Next->Pt))))
      {
        lastOK = 0;
        OutPt *tmp = pp;
        pp->Prev->Next = pp->Next;
        pp->Next->Prev = pp->Prev;
        pp = pp->Prev;
        delete tmp;
      } else if (pp == lastOK)
        break;
      else
      {
        if (!lastOK)
          lastOK = pp;
        pp = pp->Next;
      }
    }
    outrec.Pts = pp;
  }
//------------------------------------------------------------------------------

  int PointCount(OutPt *Pts)
  {
    if (!Pts)
      return 0;
    int result = 0;
    OutPt *p = Pts;
    do
    {
      result++;
      p = p->Next;
    } while (p != Pts);
    return result;
  }
//------------------------------------------------------------------------------

  void Clipper::BuildResult(Paths &polys)
  {
    polys.reserve(m_PolyOuts.size());
    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
    {
      if (!m_PolyOuts[i]->Pts)
        continue;
      Path pg;
      OutPt *p = m_PolyOuts[i]->Pts->Prev;
      int cnt = PointCount(p);
      if (cnt < 2)
        continue;
      pg.reserve(cnt);
      for (int i = 0; i < cnt; ++i)
      {
        pg.push_back(p->Pt);
        p = p->Prev;
      }
      polys.push_back(pg);
    }
  }
//------------------------------------------------------------------------------

  void Clipper::BuildResult2(PolyTree &polytree)
  {
    polytree.Clear();
    polytree.AllNodes.reserve(m_PolyOuts.size());
    //add each output polygon/contour to polytree ...
    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++)
    {
      OutRec *outRec = m_PolyOuts[i];
      int cnt = PointCount(outRec->Pts);
      if ((outRec->IsOpen && cnt < 2) || (!outRec->IsOpen && cnt < 3))
        continue;
      FixHoleLinkage(*outRec);
      PolyNode *pn = new PolyNode();
      //nb: polytree takes ownership of all the PolyNodes
      polytree.AllNodes.push_back(pn);
      outRec->PolyNd = pn;
      pn->Parent = 0;
      pn->Index = 0;
      pn->Contour.reserve(cnt);
      OutPt *op = outRec->Pts->Prev;
      for (int j = 0; j < cnt; j++)
      {
        pn->Contour.push_back(op->Pt);
        op = op->Prev;
      }
    }

    //fixup PolyNode links etc ...
    polytree.Childs.reserve(m_PolyOuts.size());
    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++)
    {
      OutRec *outRec = m_PolyOuts[i];
      if (!outRec->PolyNd)
        continue;
      if (outRec->IsOpen)
      {
        outRec->PolyNd->m_IsOpen = true;
        polytree.AddChild(*outRec->PolyNd);
      } else if (outRec->FirstLeft && outRec->FirstLeft->PolyNd)
        outRec->FirstLeft->PolyNd->AddChild(*outRec->PolyNd);
      else
        polytree.AddChild(*outRec->PolyNd);
    }
  }
//------------------------------------------------------------------------------

  void SwapIntersectNodes(IntersectNode &int1, IntersectNode &int2)
  {
    //just swap the contents (because fIntersectNodes is a single-linked-list)
    IntersectNode inode = int1; //gets a copy of Int1
    int1.Edge1 = int2.Edge1;
    int1.Edge2 = int2.Edge2;
    int1.Pt = int2.Pt;
    int2.Edge1 = inode.Edge1;
    int2.Edge2 = inode.Edge2;
    int2.Pt = inode.Pt;
  }
//------------------------------------------------------------------------------

  inline bool E2InsertsBeforeE1(TEdge &e1, TEdge &e2)
  {
    if (e2.Curr.X == e1.Curr.X)
    {
      if (e2.Top.Y > e1.Top.Y)
        return e2.Top.X < TopX(e1, e2.Top.Y);
      else
        return e1.Top.X > TopX(e2, e1.Top.Y);
    } else
      return e2.Curr.X < e1.Curr.X;
  }
//------------------------------------------------------------------------------

  bool GetOverlap(const cInt a1, const cInt a2, const cInt b1, const cInt b2,
                  cInt &Left, cInt &Right)
  {
    if (a1 < a2)
    {
      if (b1 < b2)
      {
        Left = std::max(a1, b1);
        Right = std::min(a2, b2);
      } else
      {
        Left = std::max(a1, b2);
        Right = std::min(a2, b1);
      }
    } else
    {
      if (b1 < b2)
      {
        Left = std::max(a2, b1);
        Right = std::min(a1, b2);
      } else
      {
        Left = std::max(a2, b2);
        Right = std::min(a1, b1);
      }
    }
    return Left < Right;
  }
//------------------------------------------------------------------------------

  inline void UpdateOutPtIdxs(OutRec &outrec)
  {
    OutPt *op = outrec.Pts;
    do
    {
      op->Idx = outrec.Idx;
      op = op->Prev;
    } while (op != outrec.Pts);
  }
//------------------------------------------------------------------------------

  void Clipper::InsertEdgeIntoAEL(TEdge *edge, TEdge *startEdge)
  {
    if (!m_ActiveEdges)
    {
      edge->PrevInAEL = 0;
      edge->NextInAEL = 0;
      m_ActiveEdges = edge;
    } else if (!startEdge && E2InsertsBeforeE1(*m_ActiveEdges, *edge))
    {
      edge->PrevInAEL = 0;
      edge->NextInAEL = m_ActiveEdges;
      m_ActiveEdges->PrevInAEL = edge;
      m_ActiveEdges = edge;
    } else
    {
      if (!startEdge)
        startEdge = m_ActiveEdges;
      while (startEdge->NextInAEL &&
             !E2InsertsBeforeE1(*startEdge->NextInAEL, *edge))
        startEdge = startEdge->NextInAEL;
      edge->NextInAEL = startEdge->NextInAEL;
      if (startEdge->NextInAEL)
        startEdge->NextInAEL->PrevInAEL = edge;
      edge->PrevInAEL = startEdge;
      startEdge->NextInAEL = edge;
    }
  }
//----------------------------------------------------------------------

  OutPt *DupOutPt(OutPt *outPt, bool InsertAfter)
  {
    OutPt *result = new OutPt;
    result->Pt = outPt->Pt;
    result->Idx = outPt->Idx;
    if (InsertAfter)
    {
      result->Next = outPt->Next;
      result->Prev = outPt;
      outPt->Next->Prev = result;
      outPt->Next = result;
    } else
    {
      result->Prev = outPt->Prev;
      result->Next = outPt;
      outPt->Prev->Next = result;
      outPt->Prev = result;
    }
    return result;
  }
//------------------------------------------------------------------------------

  bool JoinHorz(OutPt *op1, OutPt *op1b, OutPt *op2, OutPt *op2b,
                const IntPoint Pt, bool DiscardLeft)
  {
    Direction Dir1 = (op1->Pt.X > op1b->Pt.X ? dRightToLeft : dLeftToRight);
    Direction Dir2 = (op2->Pt.X > op2b->Pt.X ? dRightToLeft : dLeftToRight);
    if (Dir1 == Dir2)
      return false;

    //When DiscardLeft, we want Op1b to be on the Left of Op1, otherwise we
    //want Op1b to be on the Right. (And likewise with Op2 and Op2b.)
    //So, to facilitate this while inserting Op1b and Op2b ...
    //when DiscardLeft, make sure we're AT or RIGHT of Pt before adding Op1b,
    //otherwise make sure we're AT or LEFT of Pt. (Likewise with Op2b.)
    if (Dir1 == dLeftToRight)
    {
      while (op1->Next->Pt.X <= Pt.X &&
             op1->Next->Pt.X >= op1->Pt.X && op1->Next->Pt.Y == Pt.Y)
        op1 = op1->Next;
      if (DiscardLeft && (op1->Pt.X != Pt.X))
        op1 = op1->Next;
      op1b = DupOutPt(op1, !DiscardLeft);
      if (op1b->Pt != Pt)
      {
        op1 = op1b;
        op1->Pt = Pt;
        op1b = DupOutPt(op1, !DiscardLeft);
      }
    } else
    {
      while (op1->Next->Pt.X >= Pt.X &&
             op1->Next->Pt.X <= op1->Pt.X && op1->Next->Pt.Y == Pt.Y)
        op1 = op1->Next;
      if (!DiscardLeft && (op1->Pt.X != Pt.X))
        op1 = op1->Next;
      op1b = DupOutPt(op1, DiscardLeft);
      if (op1b->Pt != Pt)
      {
        op1 = op1b;
        op1->Pt = Pt;
        op1b = DupOutPt(op1, DiscardLeft);
      }
    }

    if (Dir2 == dLeftToRight)
    {
      while (op2->Next->Pt.X <= Pt.X &&
             op2->Next->Pt.X >= op2->Pt.X && op2->Next->Pt.Y == Pt.Y)
        op2 = op2->Next;
      if (DiscardLeft && (op2->Pt.X != Pt.X))
        op2 = op2->Next;
      op2b = DupOutPt(op2, !DiscardLeft);
      if (op2b->Pt != Pt)
      {
        op2 = op2b;
        op2->Pt = Pt;
        op2b = DupOutPt(op2, !DiscardLeft);
      };
    } else
    {
      while (op2->Next->Pt.X >= Pt.X &&
             op2->Next->Pt.X <= op2->Pt.X && op2->Next->Pt.Y == Pt.Y)
        op2 = op2->Next;
      if (!DiscardLeft && (op2->Pt.X != Pt.X))
        op2 = op2->Next;
      op2b = DupOutPt(op2, DiscardLeft);
      if (op2b->Pt != Pt)
      {
        op2 = op2b;
        op2->Pt = Pt;
        op2b = DupOutPt(op2, DiscardLeft);
      };
    };

    if ((Dir1 == dLeftToRight) == DiscardLeft)
    {
      op1->Prev = op2;
      op2->Next = op1;
      op1b->Next = op2b;
      op2b->Prev = op1b;
    } else
    {
      op1->Next = op2;
      op2->Prev = op1;
      op1b->Prev = op2b;
      op2b->Next = op1b;
    }
    return true;
  }
//------------------------------------------------------------------------------

  bool Clipper::JoinPoints(Join *j, OutRec *outRec1, OutRec *outRec2)
  {
    OutPt *op1 = j->OutPt1, *op1b;
    OutPt *op2 = j->OutPt2, *op2b;

    //There are 3 kinds of joins for output polygons ...
    //1. Horizontal joins where Join.OutPt1 & Join.OutPt2 are vertices anywhere
    //along (horizontal) collinear edges (& Join.OffPt is on the same horizontal).
    //2. Non-horizontal joins where Join.OutPt1 & Join.OutPt2 are at the same
    //location at the Bottom of the overlapping segment (& Join.OffPt is above).
    //3. StrictSimple joins where edges touch but are not collinear and where
    //Join.OutPt1, Join.OutPt2 & Join.OffPt all share the same point.
    bool isHorizontal = (j->OutPt1->Pt.Y == j->OffPt.Y);

    if (isHorizontal && (j->OffPt == j->OutPt1->Pt) &&
        (j->OffPt == j->OutPt2->Pt))
    {
      //Strictly Simple join ...
      if (outRec1 != outRec2)
        return false;
      op1b = j->OutPt1->Next;
      while (op1b != op1 && (op1b->Pt == j->OffPt))
        op1b = op1b->Next;
      bool reverse1 = (op1b->Pt.Y > j->OffPt.Y);
      op2b = j->OutPt2->Next;
      while (op2b != op2 && (op2b->Pt == j->OffPt))
        op2b = op2b->Next;
      bool reverse2 = (op2b->Pt.Y > j->OffPt.Y);
      if (reverse1 == reverse2)
        return false;
      if (reverse1)
      {
        op1b = DupOutPt(op1, false);
        op2b = DupOutPt(op2, true);
        op1->Prev = op2;
        op2->Next = op1;
        op1b->Next = op2b;
        op2b->Prev = op1b;
        j->OutPt1 = op1;
        j->OutPt2 = op1b;
        return true;
      } else
      {
        op1b = DupOutPt(op1, true);
        op2b = DupOutPt(op2, false);
        op1->Next = op2;
        op2->Prev = op1;
        op1b->Prev = op2b;
        op2b->Next = op1b;
        j->OutPt1 = op1;
        j->OutPt2 = op1b;
        return true;
      }
    } else if (isHorizontal)
    {
      //treat horizontal joins differently to non-horizontal joins since with
      //them we're not yet sure where the overlapping is. OutPt1.Pt & OutPt2.Pt
      //may be anywhere along the horizontal edge.
      op1b = op1;
      while (op1->Prev->Pt.Y == op1->Pt.Y && op1->Prev != op1b && op1->Prev != op2)
        op1 = op1->Prev;
      while (op1b->Next->Pt.Y == op1b->Pt.Y && op1b->Next != op1 && op1b->Next != op2)
        op1b = op1b->Next;
      if (op1b->Next == op1 || op1b->Next == op2)
        return false; //a flat 'polygon'

      op2b = op2;
      while (op2->Prev->Pt.Y == op2->Pt.Y && op2->Prev != op2b && op2->Prev != op1b)
        op2 = op2->Prev;
      while (op2b->Next->Pt.Y == op2b->Pt.Y && op2b->Next != op2 && op2b->Next != op1)
        op2b = op2b->Next;
      if (op2b->Next == op2 || op2b->Next == op1)
        return false; //a flat 'polygon'

      cInt Left, Right;
      //Op1 --> Op1b & Op2 --> Op2b are the extremites of the horizontal edges
      if (!GetOverlap(op1->Pt.X, op1b->Pt.X, op2->Pt.X, op2b->Pt.X, Left, Right))
        return false;

      //DiscardLeftSide: when overlapping edges are joined, a spike will created
      //which needs to be cleaned up. However, we don't want Op1 or Op2 caught up
      //on the discard Side as either may still be needed for other joins ...
      IntPoint Pt;
      bool DiscardLeftSide;
      if (op1->Pt.X >= Left && op1->Pt.X <= Right)
      {
        Pt = op1->Pt;
        DiscardLeftSide = (op1->Pt.X > op1b->Pt.X);
      } else if (op2->Pt.X >= Left && op2->Pt.X <= Right)
      {
        Pt = op2->Pt;
        DiscardLeftSide = (op2->Pt.X > op2b->Pt.X);
      } else if (op1b->Pt.X >= Left && op1b->Pt.X <= Right)
      {
        Pt = op1b->Pt;
        DiscardLeftSide = op1b->Pt.X > op1->Pt.X;
      } else
      {
        Pt = op2b->Pt;
        DiscardLeftSide = (op2b->Pt.X > op2->Pt.X);
      }
      j->OutPt1 = op1;
      j->OutPt2 = op2;
      return JoinHorz(op1, op1b, op2, op2b, Pt, DiscardLeftSide);
    } else
    {
      //nb: For non-horizontal joins ...
      //    1. Jr.OutPt1.Pt.Y == Jr.OutPt2.Pt.Y
      //    2. Jr.OutPt1.Pt > Jr.OffPt.Y

      //make sure the polygons are correctly oriented ...
      op1b = op1->Next;
      while ((op1b->Pt == op1->Pt) && (op1b != op1))
        op1b = op1b->Next;
      bool Reverse1 = ((op1b->Pt.Y > op1->Pt.Y) ||
                       !SlopesEqual(op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange));
      if (Reverse1)
      {
        op1b = op1->Prev;
        while ((op1b->Pt == op1->Pt) && (op1b != op1))
          op1b = op1b->Prev;
        if ((op1b->Pt.Y > op1->Pt.Y) ||
            !SlopesEqual(op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange))
          return false;
      };
      op2b = op2->Next;
      while ((op2b->Pt == op2->Pt) && (op2b != op2))
        op2b = op2b->Next;
      bool Reverse2 = ((op2b->Pt.Y > op2->Pt.Y) ||
                       !SlopesEqual(op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange));
      if (Reverse2)
      {
        op2b = op2->Prev;
        while ((op2b->Pt == op2->Pt) && (op2b != op2))
          op2b = op2b->Prev;
        if ((op2b->Pt.Y > op2->Pt.Y) ||
            !SlopesEqual(op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange))
          return false;
      }

      if ((op1b == op1) || (op2b == op2) || (op1b == op2b) ||
          ((outRec1 == outRec2) && (Reverse1 == Reverse2)))
        return false;

      if (Reverse1)
      {
        op1b = DupOutPt(op1, false);
        op2b = DupOutPt(op2, true);
        op1->Prev = op2;
        op2->Next = op1;
        op1b->Next = op2b;
        op2b->Prev = op1b;
        j->OutPt1 = op1;
        j->OutPt2 = op1b;
        return true;
      } else
      {
        op1b = DupOutPt(op1, true);
        op2b = DupOutPt(op2, false);
        op1->Next = op2;
        op2->Prev = op1;
        op1b->Prev = op2b;
        op2b->Next = op1b;
        j->OutPt1 = op1;
        j->OutPt2 = op1b;
        return true;
      }
    }
  }
//----------------------------------------------------------------------

  static OutRec *ParseFirstLeft(OutRec *FirstLeft)
  {
    while (FirstLeft && !FirstLeft->Pts)
      FirstLeft = FirstLeft->FirstLeft;
    return FirstLeft;
  }
//------------------------------------------------------------------------------

  void Clipper::FixupFirstLefts1(OutRec *OldOutRec, OutRec *NewOutRec)
  {
    //tests if NewOutRec contains the polygon before reassigning FirstLeft
    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
    {
      OutRec *outRec = m_PolyOuts[i];
      OutRec *firstLeft = ParseFirstLeft(outRec->FirstLeft);
      if (outRec->Pts && firstLeft == OldOutRec)
      {
        if (Poly2ContainsPoly1(outRec->Pts, NewOutRec->Pts))
          outRec->FirstLeft = NewOutRec;
      }
    }
  }
//----------------------------------------------------------------------

  void Clipper::FixupFirstLefts2(OutRec *InnerOutRec, OutRec *OuterOutRec)
  {
    //A polygon has split into two such that one is now the inner of the other.
    //It's possible that these polygons now wrap around other polygons, so check
    //every polygon that's also contained by OuterOutRec's FirstLeft container
    //(including 0) to see if they've become inner to the new inner polygon ...
    OutRec *orfl = OuterOutRec->FirstLeft;
    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
    {
      OutRec *outRec = m_PolyOuts[i];

      if (!outRec->Pts || outRec == OuterOutRec || outRec == InnerOutRec)
        continue;
      OutRec *firstLeft = ParseFirstLeft(outRec->FirstLeft);
      if (firstLeft != orfl && firstLeft != InnerOutRec && firstLeft != OuterOutRec)
        continue;
      if (Poly2ContainsPoly1(outRec->Pts, InnerOutRec->Pts))
        outRec->FirstLeft = InnerOutRec;
      else if (Poly2ContainsPoly1(outRec->Pts, OuterOutRec->Pts))
        outRec->FirstLeft = OuterOutRec;
      else if (outRec->FirstLeft == InnerOutRec || outRec->FirstLeft == OuterOutRec)
        outRec->FirstLeft = orfl;
    }
  }

//----------------------------------------------------------------------
  void Clipper::FixupFirstLefts3(OutRec *OldOutRec, OutRec *NewOutRec)
  {
    //reassigns FirstLeft WITHOUT testing if NewOutRec contains the polygon
    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
    {
      OutRec *outRec = m_PolyOuts[i];
      OutRec *firstLeft = ParseFirstLeft(outRec->FirstLeft);
      if (outRec->Pts && firstLeft == OldOutRec)
        outRec->FirstLeft = NewOutRec;
    }
  }
//----------------------------------------------------------------------

  void Clipper::JoinCommonEdges()
  {
    for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
    {
      Join *join = m_Joins[i];

      OutRec *outRec1 = GetOutRec(join->OutPt1->Idx);
      OutRec *outRec2 = GetOutRec(join->OutPt2->Idx);

      if (!outRec1->Pts || !outRec2->Pts)
        continue;
      if (outRec1->IsOpen || outRec2->IsOpen)
        continue;

      //get the polygon fragment with the correct hole state (FirstLeft)
      //before calling JoinPoints() ...
      OutRec *holeStateRec;
      if (outRec1 == outRec2)
        holeStateRec = outRec1;
      else if (OutRec1RightOfOutRec2(outRec1, outRec2))
        holeStateRec = outRec2;
      else if (OutRec1RightOfOutRec2(outRec2, outRec1))
        holeStateRec = outRec1;
      else
        holeStateRec = GetLowermostRec(outRec1, outRec2);

      if (!JoinPoints(join, outRec1, outRec2))
        continue;

      if (outRec1 == outRec2)
      {
        //instead of joining two polygons, we've just created a new one by
        //splitting one polygon into two.
        outRec1->Pts = join->OutPt1;
        outRec1->BottomPt = 0;
        outRec2 = CreateOutRec();
        outRec2->Pts = join->OutPt2;

        //update all OutRec2.Pts Idx's ...
        UpdateOutPtIdxs(*outRec2);

        if (Poly2ContainsPoly1(outRec2->Pts, outRec1->Pts))
        {
          //outRec1 contains outRec2 ...
          outRec2->IsHole = !outRec1->IsHole;
          outRec2->FirstLeft = outRec1;

          if (m_UsingPolyTree)
            FixupFirstLefts2(outRec2, outRec1);

          if ((outRec2->IsHole ^ m_ReverseOutput) == (Area(*outRec2) > 0))
            ReversePolyPtLinks(outRec2->Pts);

        } else if (Poly2ContainsPoly1(outRec1->Pts, outRec2->Pts))
        {
          //outRec2 contains outRec1 ...
          outRec2->IsHole = outRec1->IsHole;
          outRec1->IsHole = !outRec2->IsHole;
          outRec2->FirstLeft = outRec1->FirstLeft;
          outRec1->FirstLeft = outRec2;

          if (m_UsingPolyTree)
            FixupFirstLefts2(outRec1, outRec2);

          if ((outRec1->IsHole ^ m_ReverseOutput) == (Area(*outRec1) > 0))
            ReversePolyPtLinks(outRec1->Pts);
        } else
        {
          //the 2 polygons are completely separate ...
          outRec2->IsHole = outRec1->IsHole;
          outRec2->FirstLeft = outRec1->FirstLeft;

          //fixup FirstLeft pointers that may need reassigning to OutRec2
          if (m_UsingPolyTree)
            FixupFirstLefts1(outRec1, outRec2);
        }

      } else
      {
        //joined 2 polygons together ...

        outRec2->Pts = 0;
        outRec2->BottomPt = 0;
        outRec2->Idx = outRec1->Idx;

        outRec1->IsHole = holeStateRec->IsHole;
        if (holeStateRec == outRec2)
          outRec1->FirstLeft = outRec2->FirstLeft;
        outRec2->FirstLeft = outRec1;

        if (m_UsingPolyTree)
          FixupFirstLefts3(outRec2, outRec1);
      }
    }
  }

//------------------------------------------------------------------------------
// ClipperOffset support functions ...
//------------------------------------------------------------------------------

  DoublePoint GetUnitNormal(const IntPoint &pt1, const IntPoint &pt2)
  {
    if (pt2.X == pt1.X && pt2.Y == pt1.Y)
      return DoublePoint(0, 0);

    double Dx = (double) (pt2.X - pt1.X);
    double dy = (double) (pt2.Y - pt1.Y);
    double f = 1 * 1.0 / std::sqrt(Dx * Dx + dy * dy);
    Dx *= f;
    dy *= f;
    return DoublePoint(dy, -Dx);
  }

//------------------------------------------------------------------------------
// ClipperOffset class
//------------------------------------------------------------------------------

  ClipperOffset::ClipperOffset(double miterLimit, double arcTolerance)
  {
    this->MiterLimit = miterLimit;
    this->ArcTolerance = arcTolerance;
    m_lowest.X = -1;
  }
//------------------------------------------------------------------------------

  ClipperOffset::~ClipperOffset()
  {
    Clear();
  }
//------------------------------------------------------------------------------

  void ClipperOffset::Clear()
  {
    for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
      delete m_polyNodes.Childs[i];
    m_polyNodes.Childs.clear();
    m_lowest.X = -1;
  }
//------------------------------------------------------------------------------

  void ClipperOffset::AddPath(const Path &path, JoinType joinType, EndType endType)
  {
    int highI = (int) path.size() - 1;
    if (highI < 0)
      return;
    PolyNode *newNode = new PolyNode();
    newNode->m_jointype = joinType;
    newNode->m_endtype = endType;

    //strip duplicate points from path and also get index to the lowest point ...
    if (endType == etClosedLine || endType == etClosedPolygon)
      while (highI > 0 && path[0] == path[highI])
        highI--;
    newNode->Contour.reserve(highI + 1);
    newNode->Contour.push_back(path[0]);
    int j = 0, k = 0;
    for (int i = 1; i <= highI; i++)
      if (newNode->Contour[j] != path[i])
      {
        j++;
        newNode->Contour.push_back(path[i]);
        if (path[i].Y > newNode->Contour[k].Y ||
            (path[i].Y == newNode->Contour[k].Y &&
             path[i].X < newNode->Contour[k].X))
          k = j;
      }
    if (endType == etClosedPolygon && j < 2)
    {
      delete newNode;
      return;
    }
    m_polyNodes.AddChild(*newNode);

    //if this path's lowest pt is lower than all the others then update m_lowest
    if (endType != etClosedPolygon)
      return;
    if (m_lowest.X < 0)
      m_lowest = IntPoint(m_polyNodes.ChildCount() - 1, k);
    else
    {
      IntPoint ip = m_polyNodes.Childs[(int) m_lowest.X]->Contour[(int) m_lowest.Y];
      if (newNode->Contour[k].Y > ip.Y ||
          (newNode->Contour[k].Y == ip.Y &&
           newNode->Contour[k].X < ip.X))
        m_lowest = IntPoint(m_polyNodes.ChildCount() - 1, k);
    }
  }
//------------------------------------------------------------------------------

  void ClipperOffset::AddPaths(const Paths &paths, JoinType joinType, EndType endType)
  {
    for (Paths::size_type i = 0; i < paths.size(); ++i)
      AddPath(paths[i], joinType, endType);
  }
//------------------------------------------------------------------------------

  void ClipperOffset::FixOrientations()
  {
    //fixup orientations of all closed paths if the orientation of the
    //closed path with the lowermost vertex is wrong ...
    if (m_lowest.X >= 0 &&
        !Orientation(m_polyNodes.Childs[(int) m_lowest.X]->Contour))
    {
      for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
      {
        PolyNode &node = *m_polyNodes.Childs[i];
        if (node.m_endtype == etClosedPolygon ||
            (node.m_endtype == etClosedLine && Orientation(node.Contour)))
          ReversePath(node.Contour);
      }
    } else
    {
      for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
      {
        PolyNode &node = *m_polyNodes.Childs[i];
        if (node.m_endtype == etClosedLine && !Orientation(node.Contour))
          ReversePath(node.Contour);
      }
    }
  }
//------------------------------------------------------------------------------

  void ClipperOffset::Execute(Paths &solution, double delta)
  {
    solution.clear();
    FixOrientations();
    DoOffset(delta);

    //now clean up 'corners' ...
    Clipper clpr;
    clpr.AddPaths(m_destPolys, ptSubject, true);
    if (delta > 0)
    {
      clpr.Execute(ctUnion, solution, pftPositive, pftPositive);
    } else
    {
      IntRect r = clpr.GetBounds();
      Path outer(4);
      outer[0] = IntPoint(r.left - 10, r.bottom + 10);
      outer[1] = IntPoint(r.right + 10, r.bottom + 10);
      outer[2] = IntPoint(r.right + 10, r.top - 10);
      outer[3] = IntPoint(r.left - 10, r.top - 10);

      clpr.AddPath(outer, ptSubject, true);
      clpr.ReverseSolution(true);
      clpr.Execute(ctUnion, solution, pftNegative, pftNegative);
      if (solution.size() > 0)
        solution.erase(solution.begin());
    }
  }
//------------------------------------------------------------------------------

  void ClipperOffset::Execute(PolyTree &solution, double delta)
  {
    solution.Clear();
    FixOrientations();
    DoOffset(delta);

    //now clean up 'corners' ...
    Clipper clpr;
    clpr.AddPaths(m_destPolys, ptSubject, true);
    if (delta > 0)
    {
      clpr.Execute(ctUnion, solution, pftPositive, pftPositive);
    } else
    {
      IntRect r = clpr.GetBounds();
      Path outer(4);
      outer[0] = IntPoint(r.left - 10, r.bottom + 10);
      outer[1] = IntPoint(r.right + 10, r.bottom + 10);
      outer[2] = IntPoint(r.right + 10, r.top - 10);
      outer[3] = IntPoint(r.left - 10, r.top - 10);

      clpr.AddPath(outer, ptSubject, true);
      clpr.ReverseSolution(true);
      clpr.Execute(ctUnion, solution, pftNegative, pftNegative);
      //remove the outer PolyNode rectangle ...
      if (solution.ChildCount() == 1 && solution.Childs[0]->ChildCount() > 0)
      {
        PolyNode *outerNode = solution.Childs[0];
        solution.Childs.reserve(outerNode->ChildCount());
        solution.Childs[0] = outerNode->Childs[0];
        solution.Childs[0]->Parent = outerNode->Parent;
        for (int i = 1; i < outerNode->ChildCount(); ++i)
          solution.AddChild(*outerNode->Childs[i]);
      } else
        solution.Clear();
    }
  }
//------------------------------------------------------------------------------

  void ClipperOffset::DoOffset(double delta)
  {
    m_destPolys.clear();
    m_delta = delta;

    //if Zero offset, just copy any CLOSED polygons to m_p and return ...
    if (NEAR_ZERO(delta))
    {
      m_destPolys.reserve(m_polyNodes.ChildCount());
      for (int i = 0; i < m_polyNodes.ChildCount(); i++)
      {
        PolyNode &node = *m_polyNodes.Childs[i];
        if (node.m_endtype == etClosedPolygon)
          m_destPolys.push_back(node.Contour);
      }
      return;
    }

    //see offset_triginometry3.svg in the documentation folder ...
    if (MiterLimit > 2)
      m_miterLim = 2 / (MiterLimit * MiterLimit);
    else
      m_miterLim = 0.5;

    double y;
    if (ArcTolerance <= 0.0)
      y = def_arc_tolerance;
    else if (ArcTolerance > std::fabs(delta) * def_arc_tolerance)
      y = std::fabs(delta) * def_arc_tolerance;
    else
      y = ArcTolerance;
    //see offset_triginometry2.svg in the documentation folder ...
    double steps = pi / std::acos(1 - y / std::fabs(delta));
    if (steps > std::fabs(delta) * pi)
      steps = std::fabs(delta) * pi;  //ie excessive precision check
    m_sin = std::sin(two_pi / steps);
    m_cos = std::cos(two_pi / steps);
    m_StepsPerRad = steps / two_pi;
    if (delta < 0.0)
      m_sin = -m_sin;

    m_destPolys.reserve(m_polyNodes.ChildCount() * 2);
    for (int i = 0; i < m_polyNodes.ChildCount(); i++)
    {
      PolyNode &node = *m_polyNodes.Childs[i];
      m_srcPoly = node.Contour;

      int len = (int) m_srcPoly.size();
      if (len == 0 || (delta <= 0 && (len < 3 || node.m_endtype != etClosedPolygon)))
        continue;

      m_destPoly.clear();
      if (len == 1)
      {
        if (node.m_jointype == jtRound)
        {
          double X = 1.0, Y = 0.0;
          for (cInt j = 1; j <= steps; j++)
          {
            m_destPoly.push_back(IntPoint(
              Round(m_srcPoly[0].X + X * delta),
              Round(m_srcPoly[0].Y + Y * delta)));
            double X2 = X;
            X = X * m_cos - m_sin * Y;
            Y = X2 * m_sin + Y * m_cos;
          }
        } else
        {
          double X = -1.0, Y = -1.0;
          for (int j = 0; j < 4; ++j)
          {
            m_destPoly.push_back(IntPoint(
              Round(m_srcPoly[0].X + X * delta),
              Round(m_srcPoly[0].Y + Y * delta)));
            if (X < 0)
              X = 1;
            else if (Y < 0)
              Y = 1;
            else
              X = -1;
          }
        }
        m_destPolys.push_back(m_destPoly);
        continue;
      }
      //build m_normals ...
      m_normals.clear();
      m_normals.reserve(len);
      for (int j = 0; j < len - 1; ++j)
        m_normals.push_back(GetUnitNormal(m_srcPoly[j], m_srcPoly[j + 1]));
      if (node.m_endtype == etClosedLine || node.m_endtype == etClosedPolygon)
        m_normals.push_back(GetUnitNormal(m_srcPoly[len - 1], m_srcPoly[0]));
      else
        m_normals.push_back(DoublePoint(m_normals[len - 2]));

      if (node.m_endtype == etClosedPolygon)
      {
        int k = len - 1;
        for (int j = 0; j < len; ++j)
          OffsetPoint(j, k, node.m_jointype);
        m_destPolys.push_back(m_destPoly);
      } else if (node.m_endtype == etClosedLine)
      {
        int k = len - 1;
        for (int j = 0; j < len; ++j)
          OffsetPoint(j, k, node.m_jointype);
        m_destPolys.push_back(m_destPoly);
        m_destPoly.clear();
        //re-build m_normals ...
        DoublePoint n = m_normals[len - 1];
        for (int j = len - 1; j > 0; j--)
          m_normals[j] = DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
        m_normals[0] = DoublePoint(-n.X, -n.Y);
        k = 0;
        for (int j = len - 1; j >= 0; j--)
          OffsetPoint(j, k, node.m_jointype);
        m_destPolys.push_back(m_destPoly);
      } else
      {
        int k = 0;
        for (int j = 1; j < len - 1; ++j)
          OffsetPoint(j, k, node.m_jointype);

        IntPoint pt1;
        if (node.m_endtype == etOpenButt)
        {
          int j = len - 1;
          pt1 = IntPoint((cInt) Round(m_srcPoly[j].X + m_normals[j].X *
                                                       delta), (cInt) Round(m_srcPoly[j].Y + m_normals[j].Y * delta));
          m_destPoly.push_back(pt1);
          pt1 = IntPoint((cInt) Round(m_srcPoly[j].X - m_normals[j].X *
                                                       delta), (cInt) Round(m_srcPoly[j].Y - m_normals[j].Y * delta));
          m_destPoly.push_back(pt1);
        } else
        {
          int j = len - 1;
          k = len - 2;
          m_sinA = 0;
          m_normals[j] = DoublePoint(-m_normals[j].X, -m_normals[j].Y);
          if (node.m_endtype == etOpenSquare)
            DoSquare(j, k);
          else
            DoRound(j, k);
        }

        //re-build m_normals ...
        for (int j = len - 1; j > 0; j--)
          m_normals[j] = DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
        m_normals[0] = DoublePoint(-m_normals[1].X, -m_normals[1].Y);

        k = len - 1;
        for (int j = k - 1; j > 0; --j)
          OffsetPoint(j, k, node.m_jointype);

        if (node.m_endtype == etOpenButt)
        {
          pt1 = IntPoint((cInt) Round(m_srcPoly[0].X - m_normals[0].X * delta),
                         (cInt) Round(m_srcPoly[0].Y - m_normals[0].Y * delta));
          m_destPoly.push_back(pt1);
          pt1 = IntPoint((cInt) Round(m_srcPoly[0].X + m_normals[0].X * delta),
                         (cInt) Round(m_srcPoly[0].Y + m_normals[0].Y * delta));
          m_destPoly.push_back(pt1);
        } else
        {
          k = 1;
          m_sinA = 0;
          if (node.m_endtype == etOpenSquare)
            DoSquare(0, 1);
          else
            DoRound(0, 1);
        }
        m_destPolys.push_back(m_destPoly);
      }
    }
  }
//------------------------------------------------------------------------------

  void ClipperOffset::OffsetPoint(int j, int &k, JoinType jointype)
  {
    //cross product ...
    m_sinA = (m_normals[k].X * m_normals[j].Y - m_normals[j].X * m_normals[k].Y);
    if (std::fabs(m_sinA * m_delta) < 1.0)
    {
      //dot product ...
      double cosA = (m_normals[k].X * m_normals[j].X + m_normals[j].Y * m_normals[k].Y);
      if (cosA > 0) // angle => 0 degrees
      {
        m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
                                      Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
        return;
      }
      //else angle => 180 degrees
    } else if (m_sinA > 1.0)
      m_sinA = 1.0;
    else if (m_sinA < -1.0)
      m_sinA = -1.0;

    if (m_sinA * m_delta < 0)
    {
      m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
                                    Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
      m_destPoly.push_back(m_srcPoly[j]);
      m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
                                    Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
    } else
      switch (jointype)
      {
        case jtMiter:
        {
          double r = 1 + (m_normals[j].X * m_normals[k].X +
                          m_normals[j].Y * m_normals[k].Y);
          if (r >= m_miterLim)
            DoMiter(j, k, r);
          else
            DoSquare(j, k);
          break;
        }
        case jtSquare:
          DoSquare(j, k);
          break;
        case jtRound:
          DoRound(j, k);
          break;
      }
    k = j;
  }
//------------------------------------------------------------------------------

  void ClipperOffset::DoSquare(int j, int k)
  {
    double dx = std::tan(std::atan2(m_sinA,
                                    m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y) / 4);
    m_destPoly.push_back(IntPoint(
      Round(m_srcPoly[j].X + m_delta * (m_normals[k].X - m_normals[k].Y * dx)),
      Round(m_srcPoly[j].Y + m_delta * (m_normals[k].Y + m_normals[k].X * dx))));
    m_destPoly.push_back(IntPoint(
      Round(m_srcPoly[j].X + m_delta * (m_normals[j].X + m_normals[j].Y * dx)),
      Round(m_srcPoly[j].Y + m_delta * (m_normals[j].Y - m_normals[j].X * dx))));
  }
//------------------------------------------------------------------------------

  void ClipperOffset::DoMiter(int j, int k, double r)
  {
    double q = m_delta / r;
    m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + (m_normals[k].X + m_normals[j].X) * q),
                                  Round(m_srcPoly[j].Y + (m_normals[k].Y + m_normals[j].Y) * q)));
  }
//------------------------------------------------------------------------------

  void ClipperOffset::DoRound(int j, int k)
  {
    double a = std::atan2(m_sinA,
                          m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y);
    int steps = std::max((int) Round(m_StepsPerRad * std::fabs(a)), 1);

    double X = m_normals[k].X, Y = m_normals[k].Y, X2;
    for (int i = 0; i < steps; ++i)
    {
      m_destPoly.push_back(IntPoint(
        Round(m_srcPoly[j].X + X * m_delta),
        Round(m_srcPoly[j].Y + Y * m_delta)));
      X2 = X;
      X = X * m_cos - m_sin * Y;
      Y = X2 * m_sin + Y * m_cos;
    }
    m_destPoly.push_back(IntPoint(
      Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
      Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
  }

//------------------------------------------------------------------------------
// Miscellaneous public functions
//------------------------------------------------------------------------------

  void Clipper::DoSimplePolygons()
  {
    PolyOutList::size_type i = 0;
    while (i < m_PolyOuts.size())
    {
      OutRec *outrec = m_PolyOuts[i++];
      OutPt *op = outrec->Pts;
      if (!op || outrec->IsOpen)
        continue;
      do //for each Pt in Polygon until duplicate found do ...
      {
        OutPt *op2 = op->Next;
        while (op2 != outrec->Pts)
        {
          if ((op->Pt == op2->Pt) && op2->Next != op && op2->Prev != op)
          {
            //split the polygon into two ...
            OutPt *op3 = op->Prev;
            OutPt *op4 = op2->Prev;
            op->Prev = op4;
            op4->Next = op;
            op2->Prev = op3;
            op3->Next = op2;

            outrec->Pts = op;
            OutRec *outrec2 = CreateOutRec();
            outrec2->Pts = op2;
            UpdateOutPtIdxs(*outrec2);
            if (Poly2ContainsPoly1(outrec2->Pts, outrec->Pts))
            {
              //OutRec2 is contained by OutRec1 ...
              outrec2->IsHole = !outrec->IsHole;
              outrec2->FirstLeft = outrec;
              if (m_UsingPolyTree)
                FixupFirstLefts2(outrec2, outrec);
            } else if (Poly2ContainsPoly1(outrec->Pts, outrec2->Pts))
            {
              //OutRec1 is contained by OutRec2 ...
              outrec2->IsHole = outrec->IsHole;
              outrec->IsHole = !outrec2->IsHole;
              outrec2->FirstLeft = outrec->FirstLeft;
              outrec->FirstLeft = outrec2;
              if (m_UsingPolyTree)
                FixupFirstLefts2(outrec, outrec2);
            } else
            {
              //the 2 polygons are separate ...
              outrec2->IsHole = outrec->IsHole;
              outrec2->FirstLeft = outrec->FirstLeft;
              if (m_UsingPolyTree)
                FixupFirstLefts1(outrec, outrec2);
            }
            op2 = op; //ie get ready for the Next iteration
          }
          op2 = op2->Next;
        }
        op = op->Next;
      } while (op != outrec->Pts);
    }
  }
//------------------------------------------------------------------------------

  void ReversePath(Path &p)
  {
    std::reverse(p.begin(), p.end());
  }
//------------------------------------------------------------------------------

  void ReversePaths(Paths &p)
  {
    for (Paths::size_type i = 0; i < p.size(); ++i)
      ReversePath(p[i]);
  }
//------------------------------------------------------------------------------

  void SimplifyPolygon(const Path &in_poly, Paths &out_polys, PolyFillType fillType)
  {
    Clipper c;
    c.StrictlySimple(true);
    c.AddPath(in_poly, ptSubject, true);
    c.Execute(ctUnion, out_polys, fillType, fillType);
  }
//------------------------------------------------------------------------------

  void SimplifyPolygons(const Paths &in_polys, Paths &out_polys, PolyFillType fillType)
  {
    Clipper c;
    c.StrictlySimple(true);
    c.AddPaths(in_polys, ptSubject, true);
    c.Execute(ctUnion, out_polys, fillType, fillType);
  }
//------------------------------------------------------------------------------

  void SimplifyPolygons(Paths &polys, PolyFillType fillType)
  {
    SimplifyPolygons(polys, polys, fillType);
  }
//------------------------------------------------------------------------------

  inline double DistanceSqrd(const IntPoint &pt1, const IntPoint &pt2)
  {
    double Dx = ((double) pt1.X - pt2.X);
    double dy = ((double) pt1.Y - pt2.Y);
    return (Dx * Dx + dy * dy);
  }
//------------------------------------------------------------------------------

  double DistanceFromLineSqrd(
    const IntPoint &pt, const IntPoint &ln1, const IntPoint &ln2)
  {
    //The equation of a line in general form (Ax + By + C = 0)
    //given 2 points (x�,y�) & (x�,y�) is ...
    //(y� - y�)x + (x� - x�)y + (y� - y�)x� - (x� - x�)y� = 0
    //A = (y� - y�); B = (x� - x�); C = (y� - y�)x� - (x� - x�)y�
    //perpendicular distance of point (x�,y�) = (Ax� + By� + C)/Sqrt(A� + B�)
    //see http://en.wikipedia.org/wiki/Perpendicular_distance
    double A = double(ln1.Y - ln2.Y);
    double B = double(ln2.X - ln1.X);
    double C = A * ln1.X + B * ln1.Y;
    C = A * pt.X + B * pt.Y - C;
    return (C * C) / (A * A + B * B);
  }
//---------------------------------------------------------------------------

  bool SlopesNearCollinear(const IntPoint &pt1,
                           const IntPoint &pt2, const IntPoint &pt3, double distSqrd)
  {
    //this function is more accurate when the point that's geometrically
    //between the other 2 points is the one that's tested for distance.
    //ie makes it more likely to pick up 'spikes' ...
    if (Abs(pt1.X - pt2.X) > Abs(pt1.Y - pt2.Y))
    {
      if ((pt1.X > pt2.X) == (pt1.X < pt3.X))
        return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
      else if ((pt2.X > pt1.X) == (pt2.X < pt3.X))
        return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
      else
        return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
    } else
    {
      if ((pt1.Y > pt2.Y) == (pt1.Y < pt3.Y))
        return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
      else if ((pt2.Y > pt1.Y) == (pt2.Y < pt3.Y))
        return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
      else
        return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
    }
  }
//------------------------------------------------------------------------------

  bool PointsAreClose(IntPoint pt1, IntPoint pt2, double distSqrd)
  {
    double Dx = (double) pt1.X - pt2.X;
    double dy = (double) pt1.Y - pt2.Y;
    return ((Dx * Dx) + (dy * dy) <= distSqrd);
  }
//------------------------------------------------------------------------------

  OutPt *ExcludeOp(OutPt *op)
  {
    OutPt *result = op->Prev;
    result->Next = op->Next;
    op->Next->Prev = result;
    result->Idx = 0;
    return result;
  }
//------------------------------------------------------------------------------

  void CleanPolygon(const Path &in_poly, Path &out_poly, double distance)
  {
    //distance = proximity in units/pixels below which vertices
    //will be stripped. Default ~= sqrt(2).

    size_t size = in_poly.size();

    if (size == 0)
    {
      out_poly.clear();
      return;
    }

    OutPt *outPts = new OutPt[size];
    for (size_t i = 0; i < size; ++i)
    {
      outPts[i].Pt = in_poly[i];
      outPts[i].Next = &outPts[(i + 1) % size];
      outPts[i].Next->Prev = &outPts[i];
      outPts[i].Idx = 0;
    }

    double distSqrd = distance * distance;
    OutPt *op = &outPts[0];
    while (op->Idx == 0 && op->Next != op->Prev)
    {
      if (PointsAreClose(op->Pt, op->Prev->Pt, distSqrd))
      {
        op = ExcludeOp(op);
        size--;
      } else if (PointsAreClose(op->Prev->Pt, op->Next->Pt, distSqrd))
      {
        ExcludeOp(op->Next);
        op = ExcludeOp(op);
        size -= 2;
      } else if (SlopesNearCollinear(op->Prev->Pt, op->Pt, op->Next->Pt, distSqrd))
      {
        op = ExcludeOp(op);
        size--;
      } else
      {
        op->Idx = 1;
        op = op->Next;
      }
    }

    if (size < 3)
      size = 0;
    out_poly.resize(size);
    for (size_t i = 0; i < size; ++i)
    {
      out_poly[i] = op->Pt;
      op = op->Next;
    }
    delete[] outPts;
  }
//------------------------------------------------------------------------------

  void CleanPolygon(Path &poly, double distance)
  {
    CleanPolygon(poly, poly, distance);
  }
//------------------------------------------------------------------------------

  void CleanPolygons(const Paths &in_polys, Paths &out_polys, double distance)
  {
    out_polys.resize(in_polys.size());
    for (Paths::size_type i = 0; i < in_polys.size(); ++i)
      CleanPolygon(in_polys[i], out_polys[i], distance);
  }
//------------------------------------------------------------------------------

  void CleanPolygons(Paths &polys, double distance)
  {
    CleanPolygons(polys, polys, distance);
  }
//------------------------------------------------------------------------------

  void Minkowski(const Path &poly, const Path &path,
                 Paths &solution, bool isSum, bool isClosed)
  {
    int delta = (isClosed ? 1 : 0);
    size_t polyCnt = poly.size();
    size_t pathCnt = path.size();
    Paths pp;
    pp.reserve(pathCnt);
    if (isSum)
      for (size_t i = 0; i < pathCnt; ++i)
      {
        Path p;
        p.reserve(polyCnt);
        for (size_t j = 0; j < poly.size(); ++j)
          p.push_back(IntPoint(path[i].X + poly[j].X, path[i].Y + poly[j].Y));
        pp.push_back(p);
      }
    else
      for (size_t i = 0; i < pathCnt; ++i)
      {
        Path p;
        p.reserve(polyCnt);
        for (size_t j = 0; j < poly.size(); ++j)
          p.push_back(IntPoint(path[i].X - poly[j].X, path[i].Y - poly[j].Y));
        pp.push_back(p);
      }

    solution.clear();
    solution.reserve((pathCnt + delta) * (polyCnt + 1));
    for (size_t i = 0; i < pathCnt - 1 + delta; ++i)
      for (size_t j = 0; j < polyCnt; ++j)
      {
        Path quad;
        quad.reserve(4);
        quad.push_back(pp[i % pathCnt][j % polyCnt]);
        quad.push_back(pp[(i + 1) % pathCnt][j % polyCnt]);
        quad.push_back(pp[(i + 1) % pathCnt][(j + 1) % polyCnt]);
        quad.push_back(pp[i % pathCnt][(j + 1) % polyCnt]);
        if (!Orientation(quad))
          ReversePath(quad);
        solution.push_back(quad);
      }
  }
//------------------------------------------------------------------------------

  void MinkowskiSum(const Path &pattern, const Path &path, Paths &solution, bool pathIsClosed)
  {
    Minkowski(pattern, path, solution, true, pathIsClosed);
    Clipper c;
    c.AddPaths(solution, ptSubject, true);
    c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
  }
//------------------------------------------------------------------------------

  void TranslatePath(const Path &input, Path &output, const IntPoint delta)
  {
    //precondition: input != output
    output.resize(input.size());
    for (size_t i = 0; i < input.size(); ++i)
      output[i] = IntPoint(input[i].X + delta.X, input[i].Y + delta.Y);
  }
//------------------------------------------------------------------------------

  void MinkowskiSum(const Path &pattern, const Paths &paths, Paths &solution, bool pathIsClosed)
  {
    Clipper c;
    for (size_t i = 0; i < paths.size(); ++i)
    {
      Paths tmp;
      Minkowski(pattern, paths[i], tmp, true, pathIsClosed);
      c.AddPaths(tmp, ptSubject, true);
      if (pathIsClosed)
      {
        Path tmp2;
        TranslatePath(paths[i], tmp2, pattern[0]);
        c.AddPath(tmp2, ptClip, true);
      }
    }
    c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
  }
//------------------------------------------------------------------------------

  void MinkowskiDiff(const Path &poly1, const Path &poly2, Paths &solution)
  {
    Minkowski(poly1, poly2, solution, false, true);
    Clipper c;
    c.AddPaths(solution, ptSubject, true);
    c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
  }
//------------------------------------------------------------------------------

  enum NodeType
  {
    ntAny, ntOpen, ntClosed
  };

  void AddPolyNodeToPaths(const PolyNode &polynode, NodeType nodetype, Paths &paths)
  {
    bool match = true;
    if (nodetype == ntClosed)
      match = !polynode.IsOpen();
    else if (nodetype == ntOpen)
      return;

    if (!polynode.Contour.empty() && match)
      paths.push_back(polynode.Contour);
    for (int i = 0; i < polynode.ChildCount(); ++i)
      AddPolyNodeToPaths(*polynode.Childs[i], nodetype, paths);
  }
//------------------------------------------------------------------------------

  void PolyTreeToPaths(const PolyTree &polytree, Paths &paths)
  {
    paths.resize(0);
    paths.reserve(polytree.Total());
    AddPolyNodeToPaths(polytree, ntAny, paths);
  }
//------------------------------------------------------------------------------

  void ClosedPathsFromPolyTree(const PolyTree &polytree, Paths &paths)
  {
    paths.resize(0);
    paths.reserve(polytree.Total());
    AddPolyNodeToPaths(polytree, ntClosed, paths);
  }
//------------------------------------------------------------------------------

  void OpenPathsFromPolyTree(PolyTree &polytree, Paths &paths)
  {
    paths.resize(0);
    paths.reserve(polytree.Total());
    //Open paths are top level only, so ...
    for (int i = 0; i < polytree.ChildCount(); ++i)
      if (polytree.Childs[i]->IsOpen())
        paths.push_back(polytree.Childs[i]->Contour);
  }
//------------------------------------------------------------------------------

  std::ostream &operator<<(std::ostream &s, const IntPoint &p)
  {
    s << "(" << p.X << "," << p.Y << ")";
    return s;
  }
//------------------------------------------------------------------------------

  std::ostream &operator<<(std::ostream &s, const Path &p)
  {
    if (p.empty())
      return s;
    Path::size_type last = p.size() - 1;
    for (Path::size_type i = 0; i < last; i++)
      s << "(" << p[i].X << "," << p[i].Y << "), ";
    s << "(" << p[last].X << "," << p[last].Y << ")\n";
    return s;
  }
//------------------------------------------------------------------------------

  std::ostream &operator<<(std::ostream &s, const Paths &p)
  {
    for (Paths::size_type i = 0; i < p.size(); i++)
      s << p[i];
    s << "\n";
    return s;
  }
//------------------------------------------------------------------------------

} //ClipperLib namespace
